兆 as (part of) a number CEDICT shows 兆 as "… / million / mega- / trillion / tera- / billion (old)".

Is it ever actually used numerically, or is it standard to use Arabic numbers (or M/T for prefixes) to eliminate ambiguity?

Speaking of ambiguity, an answer and a comment say it is more commonly used for million/mega, while another answer says trillion/tera is standard.
Outside the IT world, 1兆 is 10^12, or 1万 x 1亿. But you won't see this use very much now.

Inside the IT world, (when you talk about the size of hard disk, memory, etc ...) 1兆 is 1M, which is 1024k, approximately 10^6. The might be the more common use nowadays.

Edit:

When used in SI unit, 兆 mean 10^6 in mainland China and 10^12 in Taiwan. The use in IT world actually comes from this usage, with an altered value. It is actually part of the unit, not the number.