Same answer as FFF really. Never announced myself as a student.
I always assumed ATC people could prettey much tell your level of experience by how confident your radio work was. I didn't want 'special treatment' as I believe the best way to learn is 'in at the deep end'. I was confident during my student solos - if I didn't think I could do it, I wouldn't have attempted to.
Reading back over the above, it sounds a bit like I'm 'full of myself' - perhaps a bit over confident. I don't think so - I assure you that I wouldn't have hesitated to declare my inexperience if I'd got in any kind of trouble and really needed help.
I once had an approach controller start giving me instructions in a non-standard manner. Because I'd messed up the readback of a zone clearance into class D at an 'international airport', she read each item to me, one at a time, and insisted I read back each one before going on to the next. She spoke s l o w l y too. This made me feel like an idiot, and I made a pretty bad approach and landing because I was flustered. She must have thought 'Oh God, another student who isn't really ready' - in reality my instructor was in the right seat - giggling at my mistake. Form then on I was always a bit paranoid about getting the 'kid gloves' treatment.