Does a Stratocaster get better with age?
I give this a conditional yes. What's the condition?
The condition is that if the guitar was played regularly, even if the guitar wasn't maintained 100% properly all the time, then yes, it will age well. Otherwise, no.
I dragged out my old 1989 Squier II Stratocaster (my first guitar that I still own, bought new in 1990,) and the video above is me playing it. The pickups and electronics are all original. The tuners and bridge trem block however are not, for the reason both started crumbling apart. The tuners had plastic buttons and started disintegrating, so they were replaced with exact-fit metal ones, and the trem block that was some kind of zinc alloy that literally crumbled apart, so that was also fitted with an exact-fit replacement. Both of these items were donated from a Squier Bullet HH I bought that just happened to have parts that were identical in size and fit to the '89 (and I was obviously very happy about that.)
What gives an old guitar its character is the neck and pickups more than anything else. Older guitars that were used regularly have necks that are worn in and pickups that have had their magnetism altered over the years from regular play. When you pick up a guitar that's been well-played, you feel it and hear it...
...and that vintage well-played sound and feel is obviously not limited to just Fender and Gibson. If an electric was made well (as my Squier Strat was) and played well, then yes, the guitar will age well.
But being this article about Strats in particular, let's talk about that.
Any vintage Fender Stratocaster I see that has a selling point of "barely played" or "closet guitar" (meaning bought, played a handful of times and put in a closet for 50 years before being found again) is a guitar I know for a fact will play and sound like total crap.
Even though vintage Strats of that ilk are taken apart very carefully and restored so that everything works properly, the guitar is basically no different than a brand new Classic Series '60s Stratocaster. Actually, correction, there is one major difference. The vintage Strat has a price tag that's 2000% higher or greater (not an exaggeration) over the Classic Series.
Starting at around the late 2000s, guitar crafting reached the point where every single tiny little detail of the old vintage Strats can now be recreated in a new instrument. If you want a Strat that's absolutely identical to what was sold brand new in the '60s, you can buy it right now. And yes, it will be exactly the same as the vintage, top to bottom, inside and out. Just call up the Fender Custom Shop and order one. Or buy a Classic Series. It's that simple.
Given that's true, it puzzles me why anyone other that a guitar collector would want a barely-played real vintage. As a musician's instrument, an unplayed vintage is a total waste of money. Nothing is worn in on the guitar and as an unplayed instrument, it has no distinctive tonal character because it's unused.
This is, incidentally, why so many old Squier Strats don't have a proper sound and feel to them. There are untold thousands of those guitars that were bought, played maybe for a few months, neglected and then promptly forgotten. None of those guitars ever got the chance to be played well.
My 26-year-old Strat has been played and worn in. I have been the only owner of it. The rust on the pickup pole pieces is real. The chips and scratches in the body are real. The super-twangy sound of the pickups is real. Did it sound that way when I first got it? Heck no. It happened over time.
Basically, what I'm saying is that the guitar itself doesn't just sprout character on its own. It's the player that imbues a guitar with character. If your Strat, be it by Fender or Squier, has a feel and sound that you like, getting the guitar to have character is simple. Keep playing it. The neck will change over time, as will the sound of the pickups. It will happen.
I don't play my old Squier Strat much these days, mainly for the reason I want it to last. However, I still break her out once every few months just to keep the guitar working right. She needs some of the electronics cleaned, but other than that, she's still a really good player and sounds better than ever.