It may be possible, MySQL has several table storage engines with differing capabilities. I think the MyISAM storage engine, for instance, has a theoretical data size limit of 256TB, but it's further constrained by the maximum size of a file on your operating system. I doubt it would be usable. I'm almost certain it wouldn't be optimal.
I would definitely look at partitioning this data across multiple tables (probably even multiple DBs on multiple machines) in a way that makes sense for your keys, then federating any search results/totals/etc. you need to. Amongst other things, this allows you to do searches where each partition is searched in parallel (in the mutiple servers approach).
I'd also look for a solution that's already done the heavy lifting of partitioning and federating queries. I wonder if Google's AppEngine data store (BigTable) or the Amazon SimpleDB would be useful. They'd both limit what you could do with the data (they are not RDBMS's), but then, the sheer size is going to do that anyway.