You haven't said what method or software you use to block them. Depending on what blocker you are using and how it is configured, they may:
a) Never reach your machine
b) reach your machine and be deleted
c) reach your machine and be stored in a a "junk" folder.
Contrary to the beliefs of many, storing stuff on your machine does not slow it down.
Storing stuff in your mail folders may slow the opening and closing of your mail client (and searching for old messages), but that's all.