I'm a little confused. The problem is that you don't know how long the PC is going to be away for ?
They won't say how long it will take, possibly because the cause of the problem is not known, but if it is usable now they ought to be able to give an estimate on how long it will take to examine it. You can then decide whether you need it returned, or to go ahead with the fix.
They are going to pick it up so that is a help. Groceries and banking could be done just prior to them picking the PC up.
Maybe they could leave a courtesy PC for the duration, especially if it is going to be more than a few days ? It's worth asking given your circumstances.