Greetings edward - a GFCI breaker, in the conventional sense, needs to be mounted to a buss bar. So in that regard, no, you cannot mount a GFCI after the incoming power supply. SCRs (silicon controlled rectifiers) do require a heat sink to dissipate heat. They may also require the use of a fan depending on the load and some other ambient temperature factors.
My recommendation is - if you want to use a common GFCI for your entire brew setup - is to install a sub feed cercuit breaker panel that only serves your setup. So, you would install a 60 amp 2-pole sub panel and feed it with a 60 amp 2-pole breaker. (You will bring a common and a ground along with the two main lines. This will give you 115V also) Then you can do anything you need with the 60 amp, 220 volts available. Also, you may want to split the outgoing load into several circuits. For example: 1 power circuit for the HLT and another for the BK. Please note: for your own safety, if you are not experienced working with electricity, hire a professional electrician.
Finally, follow the recommendation that come with the SCR’s.
PS - there is no such thing as a dumb question!