Yes you can do that in Audacity, but be aware that if you want the final file as an MP3 there will be some loss of sound quality. If you want to burn the final "mix" to CD, then you can avoid the loss of sound quality issue.
The loss of sound quality is because MP3 is a "lossy" format. In order to make the file size small, some of the audio data is thrown away and the remaining data is squashed up together as tight as possible. It's the throwing away of (unimportant) audio data that reduces the sound quality, and it occurs each time the data is encoded. So the MP3 that you download will be slightly lower quality than the original CD (probably not noticeable). When you import the MP3s into Audacity they are decoded (Audacity can only work with uncompressed data), then if you Export the final mix as an MP3 the data has to be re-encoded, which means that a little bit more data is thrown away. If you repeat the process of decoding/re-encoding often enough the sound quality will become trash. To avoid the problem, export in a "lossless" format (such as WAV).
I'd suggest that you use Audacity 1.3 rather than the old 1.2.6 version. You can get it here:
http://audacityteam.org/download/
Import the MP3s into Audacity (File menu > Import > Audio)
Zoom out using the zoom (magnifying glass) buttons
Use the
Time Shift tool to drag the audio so that they line up like this:
- You don't need the labels, they're only there for illustration.
- tracks000.png (20.19 KiB) Viewed 1131 times
Note also that MP3s usually have a small amount of silence at the very beginning of the track, so if you want to create a gap-less join may need to zoom in close and make a small overlap like this:
- tracks001.png (15.84 KiB) Viewed 1131 times
I'm a big fan of club music, and in my ongoing effort to go green (and for instant gratification!) I've been downloading .mp3 versions of continuous mix CDs from Amazon when the option is available, as opposed to getting it shipped in the mail, only to be ripped to one track (as it was designed) when I receive it. My issue is that they're broken up into 12-14 tracks and I can't find a way to "join" them in Audacity. If I purchase the physical CD, iTunes will allow me to "Join CD Tracks", which works perfectly, but I'd really rather just pay to get the CD immediately and join the tracks myself (not to mention saving the time and resources of getting a physical CD to me in the mail.) Is there a way to accomplish this (seemingly) simple in Audacity? Thanks in advance for any/all guidance or instruction. 
I'll give this a shot, and thanks again for the quick reply to my post.