That is a very difficult question to answer, as there are so many variable involved. Generally speaking, heavily dynamic sites that are database driven, are poorly optimized, do not utilize caching, and are heavily trafficked are the prime candidates for trouble. I know that is not much help, but there are so many interactions that contribute to load, that is the only "general" statement I feel comfortable making.
If you don't want to use work email, and have no other email account, I suggest you complete the sign up using a "free" dreamhosters.com subdomain, and use the email address of the domain you eventually want to host on Dreamhost.
This will allow you to complete the signup with yhour current hosting/email intact, cost you nothing, and gives you a "free" place to develop/move/setup your site - when you are ready to "flip the switch" you cand then "add a domain" for the domain you want to host (your current domain) at no extra cost (if you don't use the "free" registration at sign up, you don't lose it - yhou will still get credit for the first domain you register).
That way, you avoid the email problem, a preserve your right to transfer the domain for free.