If your phone linked with your Google account then there is no problem with the market to buy new apps (by WiFi).
I use my old HTC Desire with no SIM card by WiFi without problems
But notice: After a factory reset, the Google account link with the phone, I had to set it again. And for this I needed a SIM card.
I think, after repair, your phone will get a factory reset. So you will need a SIM card to set your Google account on the phone.