I just want to be sure that if I get an account I can use this software?
After tracking down some info on SQLyog I’m afraid not. SQLyog as far as I can tell from looking at their FAQ is a Windows application, since Dreamhost run Linux it is not possible to install it. I also see that it can be installed and run under WINE, but since WINE would be considered a persistent process it would be killed off anyway.
You can’t use it directly from your DreamHost server (as Shonky suggested), but you CAN indeed connect to your DH SQL server using the SQLYog/E program. Just make sure you give your IP access to the server (under the MySQL settings in the control panel).
I use it myself… awesome program IMO