If you can lay hands on a circuit diagram (the worldofspectrum website is a great resource for all things Spectrum) you might want to check that the internal supply voltages are what they should be before inserting a known good device. But usually the risk will be very very low, especially if you only power up the machine for long enough to see whether it works or not.
It works the other way as well of course: You can try the suspect ULA in a known good Spectrum as well: In that case you already know that everything in the target machine - including the supply voltages - must be good, so if fitting the suspect ULA in that machine stops it from working, you know the ULA is bad.
The greatest risk, actually, comes from the fact that there is a right way and a wrong way round to insert the chip into the socket, and putting one in the wrong way around and applying power for any length of time very likely will damage a healthy IC. So be very careful in that respect.
Also, be careful not to fold or bend any of the device pins as you insert it into the socket - it's quite easy to do accidentally, and you can only bend IC pins back into shape one or two times before they snap off.
