Broke the fan connector off logic board

In removing the bottom case I broke the fan connector off the logic board (I didn't see that it's not necessary to disconnect this, and while I thought I was being careful, apparently not).

One of the pads came up with the connector, so will repairing it require soldering onto a very thin trace? Is this likely to be successful?

Alternatively, is it viable to just keep the unit running without the fan and the bottom case? I'll be careful to keep my fingers away to avoid a shock.