Can radar detect a small flying device with MEMS microengines?
Obviously the MEMS engine itself is not going to be detected: they're only a few millimetres across. The question entirely depends on what you attach it to.
Conventional radars have trouble detecting UAVs less than a couple of metres long, and replacing their power plants with micro turbines won't change that.

My neighbours at Aveillant already have a holographic radar system that can detect smaller targets such as UAVs more accurately. Again, changing the power plant technology won't change that.

Micro-turbines are not intended to replace propulsion systems, but to replace batteries, allowing them to use denser hydrogen, methane, or methanol fuel. As far as I've been able to find, they don't produce break-even power yet, but it's envisioned that they will become commercially relevant once they can produce more than 10 W (about .01 hp), in a few years' time. For comparison, a current, small, military UAV might generate tens of horsepower, and some experimental super-lightweight UAVs need as little as 5 hp, but with no payload or cargo.

TL;DR: (a) MEMS turbines aren't going to be relevant for UAVs for some years, and they'll have to be much bigger than they are now; (b) replacing the power plant won't make much difference to the radar signature.