Can I use iTunes Match to move my music to a new computer?

The short answer is, yes, you can.

The more complicated answer is, yes, but this is not the best way to do it. The best way to move your music to a new computer is to transfer it from the original computer. Apple has a few very helpful knowledgebase articles to help you choose the right method:

iTunes: How to move your music to a new computer

OS X: How to migrate data from another Mac using Mountain Lion and earlier

How to transfer data from a PC to a Mac

Always remember that iTunes Match is not a backup service, nor is it intended to be a transfer service. It is your responsiblility to backup your personal data locally.