I have used forstner bits to hog out a mortise before, tried it on an ash timber I was just doing some experimenting with, it will become a nice sign post eventually.

I made some mortises in it with a forstner, because I wanted to try it. I used a 1 1/2" bit, and it worked well.
Yes it can very easily wander, you just have to proceed with caution. The fact that you have to stop and clear the chips out when you go very deep is a help here, it helps you keep your hole sighted. The bit's ability to eject chips doesn't work deep in a mortise. You have to manually clean them out every now and then, which can be done by just pulling up the bit and shaking it a bit.
It seems that this would be slower, but a forstner bit can hog out wood much faster than an auger, with a lower power drill.

So my verdict is it can work, but you have to proceed very carefully. I got the bit stuck once, but managed to get it out without too much trouble.

The hardest thing with a forstner bit is to get the initial alignment right, not all of them have a spur in the middle, and even so the spur is pretty small when they do have.

I used a Freud forstner, with a wavy edge and 2 cutters.
But you have to use an extension, since they have short shafts on them.