This is a very very loaded question. So I'll answer.
Yes...
No...
Alright, now to explain.
No:
I'd say if you have a 360 or older console and happen upon a pawn shop which sells the games used and cheap (say $10 each or so) then buy them if you can. This isn't a hard and fast rule, but i do prefer physical games when it's possible.
There's also that perhaps DRM isn't always enforced, perhaps you can get the game and download it via your favorite service. Since i refuse steam, it would have to come from GoG or from Humble Bundle, and NOT a steam key.
Something to also note, some games might have viruses or unwanted malware jacked into them, while usually legit copies don't (unless you consider the DRM/Copy Protection Malware... Which some of them are)
Yes:
If you are waiting for the game to become DRM-free, or you would never touch it otherwise, i'd say yes. If i acquire a game, usually it's to try, or because i'm just not going to wait for it to come to my store of choice, remove DRM features, or wait for it to come down in price enough for it to be worth actually paying for. This doesn't mean i'm not willing to pay my dues for a dev or publisher, but it's going to be on my terms, and my terms have very strict policies. If DRM is circumvented via a pirated copy, then that perhaps is the only way to play it until the publisher/devs change their ways.
There's also the cases of some games just not being available anymore, either because hardware is scarce, the games (like Cartridges) are rare and sold on Ebay for $300+, or games locking your options behind annoying paywalls.
If you plan to buy the game later when it's on discount and DRM-free, i'd say go ahead and you'll pay when it's time. If you aren't willing to pay, well you'd never play the game otherwise, and games are meant to be played (no matter what corporation or copyright law says).
To note, i have the Mass Effect games for my 360 and i have yet to get past an hour in... So maybe you'll lost interest before you get very far. It's always possible. Or maybe you'll start playing, see them release the game DRM-free, and you'll delete your local copy the moment you buy the more genuine customer friendly copy...
Only time will tell. I won't judge you.