the device costs some $250, its a microcontroller type of gadget.
that is a lot of money to toss if they void the warrenty on you or something. soooo, i disclaim my answer based solely on its price and the manufactures suggestions. no $25 worth of alkalines would be worth the $250 , when not following manufacture recommendations, or if ever needing warrenty service.
but
i would use some regular ni-mh on it , and see how it goes, it is unlikly that it will damage the device, and i cant see how it could effect the calibration of it. but it Could suffer from not enough voltage.
in a device like this it could require (for 2X example) ~2.6v minimum to operate correctally, and WITH such a low drain from the device, it could run off of alkalines for a long time before dropping that low in voltage, unlike a higher drain device.
with ni-mh (or ni-cd) it may suffer from not enough voltage.
now there ARE situation where not enough voltage could cause a problem beyond not running, a microprosessor stalls , a mosfet half closed, a regulator having a fit. but so too would the alklaine reach that voltage in eventuality.
i would assume if there was ever a problem, it will be from to low of voltage in this situation.
that would be the biggest difference, the alkaline would start out at ~1.5v , and given a LOAD it would drop down in voltage , but small gadgets dont have a big load. so it stays at ~1.5v for a long time then wanes down slowly to ~1.0-.9v before it is pretty much dead.
a Ni-Mh AAA would start with a max voltage of about ~1.4v and decline quick to ~1.2v and hold that ~1.2v for a long time then get to about ~.9v as it was dying.
if it is a 4xAAA device, then you might have the issues of reverse charge , when the battery set is allowed to discharge to far down, that CAN be another reason why a certian battery is defined by the manufacture, just so the care and feeding of the device is simplified.