Question about a vax

Hi all. This is probably a stupid question for some of you who know
drugs and interactions, reactions but I thought I'd ask. Shamrock has
an appt tomorrow night for his FeLV booster (necessary living with a
FeLV+ cat) and he's due for a dental but I'm not scheduling them
together so we'll schedule that tomorrow after his jab. He also is
unable to clear the latest allergy attack (it may not be tuna
afterall?) and is pulling his fur out again and has sores again so he
needs a depo shot (I think that is the steroid). Is getting a vax and
a steroid shot together going to render the FeLV booster ineffective?
I set up the appt with the receptionist so she didn't mention it and I
would hope the vet will when he comes in, but what do you think?