Ya dude

Yes.

 I bought Starcraft II on Launch day and played the first 4 or 5 missions having never finished the original.  I've since gone back and finished the entirety of the Terran campaign and 8 missions of the Zerg campaign and I find it amazing how well the original holds up.  My eyes have adjusted to the blocky sprite and textures and I'm finding that I'm having a blast.  It's well worth it to get the battle chest, regardless of whether or not your computer can run SC2. $20 is great value for what you'll get out of  it.   
 
On a separate note, there is actually a Starcraft 2 demo available.  Just not the conventional kind, but a friend of mine just bought a new video card and there was a disc on it with a timed demo.  I don`t remember the exact details, but I think you get 7 hours or so before the demo times out, so if you can get your hands on that, it would be a great way to see if your system can handle it.    
 
Also, here`s a handy link:   http://www.srtest.com/cyri    
    
Just pick Starcraft II from the drop down menu and it`ll give you a pretty detailed list of how all of your components stack up. 
 
If you can end up running Starcraft 2, I`d suggest you get the battlechest as well anyway.  It`s a classic and the gameplay holds up phenomenally well.  

Yea most definitely.  I am basically in the same boat as you.  Only when StarCraft had first come out, I dipped my feet in the water a little bit.  Definitely a fun game, but I was too young to understand the gameplay mechanics and story.  Now being 23 and StarCraft 2 having been released, I figured I would not only dip my feet in, but take a dive.  I bought the Battle Chest last week and have been powering through the Terran campaign so far every chance I get.  StarCraft II: Wings of Liberty was actually dropped off at my doorstep today.  I will be installing it as soon as I get home from work and play a few rounds online.  After that, I'm getting right back into the original storyline on StarCraft, then play through Brood War's campaign, then on to StarCraft II: Wings of Liberty campaign.  Now that I look for and appreciate amazing gameplay, I don't know why I ever stopped caring so much about StarCraft which ended up with me losing it. 
 
FUCKING BUY THE BATTLE CHEST, THEN FUCKING BUY STARCRAFT II: WINGS OF LIBERTY