My trem equipped guitars get a lot more play than my LP or tele.
I would say you're not going to get close to Van Halen territory with a squire generally, especially one that hasn't had a ton of attention paid to the nut, but my S type with a Gotoh 510 and Jazzmaster with the stock Fender system and a Graphtech XL nut and a Mastery bridge both stay in tune no matter how much shoegazing I do. Not VH dive bombs sure, but I'm not precious about it by any means.
I think if you're looking for crazy dive bombs you're going to be disappointed by most non locking systems, but for real just try some subtle warbling now and then, it's fun.