Yes, you can do this.
Two ways as of right now, both with rather serious limitations.
A) Motorola's solution is to purchase a M470 (MCS2000 style), an Iden specific BIM, and a few other auxillary boards and interfaces you'll need to make this work (As Bruce provided you above) You cannot use a M370. This will get you caller id, with alias resolution from your ADM, just as any other MDC or ASTRO would. You can switch between private and group calls from the resource on the screen, and use it as a patch group. It is very pricey. Over 10K, without considering any firmware upgrades your OP's may need, or software.
Main drawback. NO crossfleet. No way no how. Moto will be happy to sell you a M470, but any firmware upgrade for a crossfleet capable unit is pretty much out of the question. Also, considering the M470 is not GPS capable for 911, you may run into issues gettting it activated, depending in your IDEN provider.
B) A few other aftermarket vendors have interfaced A I305/315/325PS to a standard tone remote interface. Then, it acts like a regular 4 wire resource. You'll have no way to manupulate the functions on the radio itself, unless it is mounted to where you can physically access it (so putting it in the ceb rack would limit you to one group, but in your case, it sounds like that could work). Much more reasonable price.
Zetron has a complete, crossfleet capable console solution that works identically to Moto's, complete control of the radio remotely, etc. And Motorola *Does not even have that for thier own product line*. Go figure.
PM me for other specifics if you may need them. I have seen both work.
All this is out the window for the new generation consoles. IDEN interface should be fully supported again, with current run subscribers, with crossfleet capability, etc. As usual, too late. /\/\ has lost several large console sales because of this problem.

The internal product groups dont really work together, obviously.
FYI, You can also interface a Iden resource to the Motobridge interop radio switch product, with full control.