very possible. when tiels get the vibes, they can start laying even on cage bottoms. like mentioned above, i suggest avoiding any nest-like items or encouraging egg laying. in captivity, the egg laying can get out of hand really quick, and the chance for the female to die becomes very high. in nature, cold weather and the lack of food acts as an automatic sign for the female to stop laying. this is not always the case in captivity, as they technically live in permanent summer (unless you simulate winter).
if the idea is to figure out is your tiel a male or female without taking a test, you can just wait for them to grow up a bit. males have very characteristic behavior, and you should be able to tell in no time if he is a male or female.
it also seems (and this may very well be disproven so take it with a grain of salt) that female tiels have large yellow (or white in the case of whitefaced) spots on their primaries and secondaries. the males as babies have these too, but significantly smaller. they disappear as they molt to their adult feathers. i sexed my 2 month old with that, and was correct. of course this was only once, so there is large room for errors.
i cannot find the specific image to attach here im afraid.