No, all your sites are on shared servers, so there won’t be any slowdown because your account has many sites. Performance is limited by the performance of the shared servers and the speed of connection to the servers.
Arguably if you’re on a shared server with a high traffic web site also on it, performance will be affected on all other sites on the shared server. Dreamhost is quite good at monitoring this, and the servers now are much faster and more reliable than 2 years ago. 2-3 years ago a lot of customers complained about downtime and slow web site speeds. I haven’t seen any such chat on this forum for a long time now.
Ultimately you aren’t going to want to run a major commercial web site from a shared server, but for most web sites with a few hundred users a day/month, shared services are easily sufficient.