Ive done this exactly
I have an 08 Tahoe, I just recently had Alpine Type R speakers installed, The front components were about $250 and the rears were $150. I am keeping the stock head unit and didnt want to buy an amp. Ive ran subs for about 8 years and im tired of the long run rattling and space that they can take up. The new speakers can handle about 110 watts (rms) and the stock head unit and amp are only pushing about 15 watts to each speaker. It sounds like crap, after spending about $600 for the speakers, install and tax it was a horrible idea cause i didnt want to buy an amp. The stock speakers were sooo much louder, these new speakers can handle so much more then theyre getting so I have to get a 4 channel amp that can push at least 100 watts rms to each speaker, but when i get the amp installed this weekend it will be well worth it and i'd say a total of about $1000 for the system but thats ok cause I had the new speakers installed cause they just werent for me since im not running subs, if i was the stock speakers were fine as far as loudness and treble was concerned. If you dont want subs but you want your door speakers louder, you MUST also buy an amp!!!