Yes you can add your own cig-bin and/or your own formmail script. In fact, due to Dreamhost's use of suexec, which runs cgi scripts as your user, you can run your formail script directly from any web accessible directory without having to place the script into a cgi-bin directory.
That said, it does not necessarily mean you should do so, as formmail scripts are notorious for being hacked and exploited. The Dreamhost provided formmail script is pretty robust. I have hosted here for many years and never had it exploited; I have (unfortunately!) had a "popular" and commonly used formmail script exploited on one occasion.
If you can manage it, I strongly advise you select "point 1" of the Freeway documentation to follow ("1. Your ISP has a pre-configuered script in place already for you."). I think that doing it that way, while it might initially seem slightly more complicated, provides a level of known security that you may not get if you take the other approaches.
There is quite of bit of help available in these forums on the use of form mail scripts, some of which might be of help. Good Luck!