Can I access my entire iTunes library if I don't have all of the computers any more

Hello!

I have an extensive collection of songs on iTunes that I have put together over several years.

I was looking at the iTunes Match with the storage in the Cloud, and that looks pretty good.

But my problem is that I no longer have some of the older computers, and my new ones don't have the entire library.

Would iTunes Match solve this problem, please?

Thanks in advance,

Sincerely,

Erin