diyAudio - Briefcase BOOMBOX build!

Hey guys this is my first post. I have done a far bit of research and just have a few specific questions.

If i use this amp, without a crossover, can i hook up tweeters and a woofer. Or must the speakers be extended range?

As in will it sound bad because high frequencies are being sent to the woofer and low frequencies to the tweeters?

this is the amp
Dayton Audio DTA-2 Class T Digital Audio Amplifier Module 300-385

this is the tweeter
2" Treated Paper Cone Tweeter 279-024

this is the woofer
GRS 4PF-8 4" Paper Cone Foam Surround Woofer 292-404

Also any tips for making the cheapest possible boombox in a briefcase would be appreciated. Thanks