I've adjusted Strats that were in tune. You just need to make sure that the screwdriver is a perfect fit, so it doesn't strip the screwhead. ...but that applies to any situation where you use a screwdriver. The proper screwdriver head in the proper screw, can't strip out,...in my experience. It grips too well to 'skip' across the screw. ...that being said,..if I were tightening the claw (which would raise the string pitch even higher,..increasing the tension)...then yeah I'd loosen the strings first. ...that was one of the things the bugged the sh*t out of me about Strats,...actually maybe the only thing. I had to do setups on it at least once a month because the saddles would move. And then instead of adjusting 2 screws (like on an LP) you're adjust 12 tiny little allen screws,..2 in each saddle. That got real old real quick. I prefer the sound and feel of an LP,..but I LOVE how much easier they are to setup. Well cut nut, proper relief in the neck via T-rod adjustment, and set the bridge/string height? That's it,...You're off and racing. No constant tuning and retuning,..adjusting a couple things, retuning,..adjusting a couple things,..retuning. Strats are great guitars,...but damn they're a lot of work to keep running in a perfect and optimal state. ...at least in my experience. It became a real chore keeping it optimal 100% of the time.