You're adding speakers with bigger magnets, stiffer surrounds, and stiffer cones that will need more power to sound the way they're supposed to. Will they play music? Sure. But adding an amp should be the first order of business, IMO. Without an amp, you might get slightly better highs, but your mid- and low-end will disappear unless you can really drive those things. Also, I'd be weary of adding crossovers to a factory system that's already probably aggressively handicapped by the OEM head unit, i.e. bass roll-off at moderate to high volumes.
I've been through all this before with my Tacoma. Did a plug-and-play amp that made the factory speakers sounds really good, but ended up amplifying the crappy OEM signal and all it's faults (got hissing, etc)...then swapped out speakers... then added an AudioControl unit to try correcting the signal...
Wasn't until I swapped to an aftermarket head unit with legitimately good, clean signal (and an amp) that the sound really came alive. But I recognize that's a lot harder to do these days with so much rest-of-car integration in factory radios. So it's all moot.