Definitely. The amp did a few things. It of course sent more power to the speakers so they could get louder, but it was also a crossover system to make the rear 6x9s act like "sub-woofers".

In your car all 6 speakers (2 tweeters, 2 front door speakers, 2 rear 6x9s) get the full range of music. Lows, mids, and highs. In a Monsoon only the front 6 (2 tweets, 2 front doors, 2 rear doors) got the full range, and the 2 rear 6x9s got only lows.

Now what this means for you is that you can buy any damn speaker you want, and it will be better than stock. Will it sound better if you put an amp to them as well? Of course, but it'* not needed if you get a great H/U. Unless you are going for the stock look but want better sound.

This is what I would get, and this is just personal opinion, so you can have a starting point.

Kenwood KDC-MP142 (kdcmp142) All In-Dash Car Stereo Receivers Car Stereo Receivers and Head Units Car Audio Car Audio, Video, & GPS Navigation - Sonic Electronix
This is a nice, good, name brand head unit for not a lot of coin. Only $80 and the only thing you don't get is Sat-Radio control included. If you want Sat-Radio control included you just spend an extra $15 for the next best head unit, and $99 on the goodies to make it work.

Kenwood KFC-6972ie (kfc6972ie) 6" x 9" Speakers Car Speakers Car Audio Car Audio, Video, & GPS Navigation - Sonic Electronix
Decent, but not the best, 6x9 full range speakers. I'm all about bang for my buck, and I've personally heard these babies in the stereo shop just up the road from me. The guy there sells them $100 a pair, but only $55 here.

Kicker DS650.2 (07ds6502) 6-1/2" Component Systems Car Speakers Car Audio Car Audio, Video, & GPS Navigation - Sonic Electronix
And your front door speakers. A decent component system to replace both the tweeters AND 6 1/2 speakers in the door itself.

Jensen Power 760 (power760) Multi-channel Amps Car Amplifiers Car Audio Car Audio, Video, & GPS Navigation - Sonic Electronix
An amp to run everything. I wouldn't recommend running a sub off this thing because it'* a 4 channel amp, but it would be able to run all the stuff I just listed no problem.

Note to you: I put this list together as a wish list for myself. It doesn't have the best of everything because I'm on a budget, but what I did choose isn't the bottom of the barrel either.

would those speakers still sounds good without the amp or changing the factory radio out?

Yeah they should.

Bass needs power. Power comes from amp(*). It'll be tough to get noticeably better bass without adding power.