I'm sure you'll understand that I can't give a definitive answer without seeing the full designs, but I can certainly provide some issues and concerns I would want addressed if I were consulting on such a project.
You don't define what you consider "high density", but I'm going to regard it as more than 5,000 watts per cabinet. (Some people will say that 4,000, or even 3,500 Watts, is the "break point", but those arguments are immaterial to the points I want to make.) Neither do you indicate if your CRAC units are for under-floor or overhead cooling. If under-floor, be aware that you can't properly cool a true "high density" data center using only conventional computer room air conditioner (CRAC) units – and that assumes a raised floor of 24-inches or more in height, which is unlikely in most existing rooms. If overhead cooling is to be used, then it will be necessary to use a significant amount of duct work to properly channel both the supply and return air from and back to the CRAC Units. Simply filling the room with cold air won't do it. And my first suspicion in reading your question is that filing the room with cold air is exactly what the HVAC rep has in mind by doing this. Its just not that easy. Air flow, as you properly observe, is a critical part of making high density cooling work.
There are other basic concerns about using Building Air. First, data centers are normally expected to be "closed systems". The CRAC units operate by sensing return air, and if there is other air mixing with it, then the CRAC's will be getting the wrong message. Assume for the moment that some of the cool building air mixes with the warm return air heading back to the CRAC's, cooling it down. The CRAC's will think temperatures are great, and that less cooling is necessary, and will discharge air at an elevated temperature. (We have observed situations where simply locating an outside ventilation air duct over a CRAC unit have caused erratic air conditioner performance.) Data hardware discharge air, which is probably hotter than normal office return air, will also return to the building HVAC, causing it to put out more cold air, exacerbating the problem. In short, trying to combine two disparate systems, each of which is separately controlled, but each of which may be offsetting the other, creates complications that can be extremely difficult to design around, and virtually impossible to analyze and control after the fact. It may be possible to achieve, but I wouldn't want the responsibility of trying.
Another concern is humidity control (which is why a data center should have a vapor barrier – another possible problem in an existing room"). Data centers typically operate at a constant 40% - 50% relative humidity. They also typically operate at lower discharge air temperatures than building HVAC, with a very high "sensible to latent heat ratio". (Latent heat in offices results primarily from people and perspiration, which is minimal in a Data Center. Equipment gives off 100% Sensible Heat. Any air conditioning system handles both, but the designs are different depending on the relative amounts of each.) Here again, the two systems, each intended for completely different types of operations, and will likely oppose one another.
Then there's the matter of air filtration. Data center air is heavily filtered through the CRAC units to minimize dirt accumulation in small electronic equipment fans and circuitry. Filters are changed regularly (or at least should be) to ensure a cleaner than normal environment. Foot wipe pads are usually located at data center entrances to minimize the amount of dirt on people's shoes. Building air is never so well cleaned. (Just look at the ceilings around building air grills that have been in operation for a year or more, and see the amount of dirt accumulation.)
Supplemental filters could be added before the air reaches the data center, but unless the HVAC system is designed specifically for this, and the filters regularly changed, they will probably restrict the amount of air to the point where the supplemental supply may be minimal anyway. In other words, if you depended on the cooling, and it isn't there because of the filters, you're in trouble at the outset.
There's also the matter of fire protection. Fire, and fire suppression, inside a data center must be completely contained. Therefore, all ducts entering and leaving the data center must be provided with automatic fire dampers. This is just another expense involved in trying to run building HVAC into the data center. Bringing in enough air to be worthwhile will require large ducts and, of course, large fire dampers.
And lastly, there's the ever-present question of "availability". The data center runs 24 hours, seven days a week. It may even have generator backup. Is the building air necessary to maintaining operations? If so, is it equally reliable? If it is, and it's not, then why is it being used? There are a number of very special techniques for handling high density design. I would not generally consider adding building HVAC to be one of them. The first requirement is to build an excellent "cooling foundation" with conventional CRAC units, properly sized and located relative to the equipment. The various special means of supplementing the cooling can then be added, as needed and as appropriate, depending on the actual loads, their locations, and a variety of other conditions. Building HVAC cannot provide that flexibility, even if could provide a worthwhile addition to cooling capacity, which I very much doubt it can.