Nope, they would have to let you download the song as a wav file to be close. An Mp3 can not be as good if that is what they have to sell.
No the quality will not be as good as a store boaught CD...but, depending on what equipment you play the MP3 back on will determine your satisfaction. If you use a high-end system for playback, you will be very disappointed. If you play it back on an ordinary "hi-fi" system, typical car system, or boombox, then you will probably not be able to tell the difference from the store bought counterpart.
This seems to always be more complicated than people make it out to be. I agree with much of what Seasoned says, but the assumptions always seem to be that one will be downloading music in mp3 format. Now, this may be what you are looking to do, and if so, then I suggest you look into other formats for downloading music. These are larger files that have been compressed much less than "standard" mp3 files. As a result, they take longer to download (generally some sort of cable or DSL modem is required), and they produce better quality recordings when decompressed into standard WAV or AIFF files.
The formats that I am familiar with (and use) are FLAC and SHN (shorten). SHN was the standard for "lossless" digital over the internet for a long time, but people seem to be moving to FLAC nowadays. I believe for its ease of use.
You can find out more info on these formats by looking at http://www.etree.org This site contains links to excellent faq's on these formats, and it also includes info on how to get involved downloading music from bands that allow (legally) the free use and distribution of their shows in these formats.
Those who have fast connections and want to see how good it can be, check out some tunes from the following links. (Note that I have suggested these based on sound quality alone. Better performances from these bands do exist, as do better recordings).
For KVHW (an excellent, now defunct band with Ray White (formerly with Zappa) and Steve Kimock (a truly excellent guitarist)), check out something from their 12-10-99 show at:
For another Steve Kimock performance from a more recent band of his, aptly called the Steve Kimock Band, check out his 02-04-02 performance at:
For a small sampling of what else is legally available in these formats, check out:
That is just a start. Poking around on the internet will help you learn much more, more useful information about these formats. Also, keep in mind that the links I have provided are to recordings by enthusiasts (albeit extremely talented ones), not by "professional" recorders. They are just samples of how much better SHN can be than MP3. Those who tend to conflate internet music with MP3 and who have the capabilities to do so should really look into these other formats.
(Caveats: You will need a copy of shorten to decompress the files from these links. It is freely available through www.etree.org. Also, to get the best results, of course, you need good software and hardware for burning. Drives do matter.)
In response to your question: probably not. There is no standard for the pay download sites. I know Mac has that mp3 download service that you pay for, and I also know that Phish has started releasing all of their shows for download via both FLAC and MP3. These are both pay services. You'll need to check each site for the details. Personally I stick to the free stuff, as I can find "decent" copies (or copies that will just allow me to listen that one time) for free elsewhere of the music that most interests me.
I would suggest that downloading from the internet, along with the monumental greed of the music industry has led to a miserable state of affairs for the buyer of anything other than "kid music". Where are the CD and record stores we loved to visit? Gone with the wind!!! Only the full-price outlets like Tower Records are left! The kind of store where you could get personal service from knowledgable staff, lots of product (including special deals on new-releases), and plenty of classical, jazz etc. is a thing of the past. Only mail and on-line retailers are left, and, of course, the subject of this thread... low-fi downloading. Aaargh, Yuck, and a pox on their heads!!!