Absolutely. This is especially crucial with the strat. I'm primarily a strat player, and if the guitar doesn't ring acoustically, it's not going to magically sound better when amplified. I modify pretty much all of my strats, usually starting with the pickups. My main guitar is a late 80s "ultra" model that was built in the custom shop. It originally came equipped with Lace Sensor pickups in a HSS configuration. I never liked them, but the guitar was amazing unplugged, and I knew I could replace the pickups for much better tone. I installed a set of (all single coil) Fralins, and it's the best strat in my collection now.
So I'd recommend playing several guitars and finding the one that feels great and sounds great unplugged. They it plugged in as well. Get a feel for how it replicates what YOU think "classic tone"is. Pickups are a straight-forward replacement option, and a lot of players swap them out.
Locking tuners are pretty handy on a strat, and will contribute to better tuning stability. There are also options for the trem bridge that you might explore down the road. I like the stock 2-point trem on my main guitar, but I also have other strats with the standard 6 screw trems, and they're great. Each of my strats is different, and has its own personality.
