While not at the level of Cappielow I've handled submitting and seeing to completion (insurance back-and-forth, getting the check from the insurer, getting the repairs done, figuring out what to do with the small excess amount we had left over) a claim for a business that suffered pretty severe roof damage. Leaving aside the obvious legal differences between Texas and Scotland:
Sure, all else being equal (own the property, no planning permission stuff etc.) you can fix anything you want whenever you want.
It wouldn't ruin our claim necessarily. Presumably (and this is a presumption) the insurer has already been out to have a look and has got the evidence they need. If that's the case it doesn't matter if we start repairing it now.
But if the club is still waiting on the insurer to decide on a payout, they may decide - and I'd agree with them if they did - it's far too risky to start repairs now. We do have a bit of cash in the bank but we need to be prudent with it, and the most prudent thing right now is to wait for insurance to run its course.
That's what I picked up as well, it's "will the money we get from the insurer allow us to do more than simply patch up the roof here?" If that's the case it's all the more reason to wait - no point in getting someone up there to just patch it up, then finding out there's scope to do more work and having to go through it again.
The only thing I find strange is how slowly the insurer is moving, but I've never made a roof claim in Scotland so maybe it's not a fair basis for comparison.