Yes, but within reason. Anything you buy that is clearly essential they are not going to quibble with. Buy what you need; keep the receipts and submit copies; that's what they will base the decision on reimbursement on.

Note that this isn't an excuse to go to town and buy an entire new wardrobe; if your travel was for a particular event (wedding, job interview, etc) then you have a stronger case for being a little more extravagant and buying an outfit that otherwise may have no chance of being reimbursed.

Also, don't expect a speedy response to your reimbursement claim. It's highly unlikely to be paid out in the timescale of days; besides, you'd be advised not to submit a claim at all until either a) your luggage arrives or b) you're back at home; you'd be advised to file a single claim, rather than claiming every day, or every couple of days, for any new items you may have had to buy while awaiting your luggage (and hopefully it turns up soon!)

As the previous poster noted, remember that your travel insurance may pick up any additional expenses that the airline won't cover.