There are a couple of potential issues here.
1.) I would be shocked if any AHJ would allow you to tie directly to an initiating device. I have never explored the code to see if this is explicitly disallowed, but I would be shocked if it's not. With that said, a very simple (and reasonably inexpensive) relay can be added at just about any location, and that relay CAN, in most cases, be pulled directly from an initiating loop.
TL;DR - Bring in a licensed fire alarm company to install a relay for this purpose.
2.) Shannon points out that the stairwells must have positive latching, which a maglock does not provide. You have a few options here -
A. Install a fail-safe electrified trim retrofit onto the existing crashbar, and use that to control access instead of a maglock. (Side note - never use maglocks. Ever.)
B. If you're dead set on doing it the wrong way and using a maglock for some bizarre reason, you may have a potential code issue even then, as you will likely NOT be able to use two separate latching mechanisms on the same door. Some AHJ's will approve a passage latchset that will just latch the door shut but can be operated from either side, but most will not in my experience. In other words, you may have no choice but to do it the "right" way and use an electrified exit device.