So much mis-information, so little time :)
With regards to the OP's primary question, yes, radiant (be it electric or hydronic) can be the primary heat for a room. The only way to know for sure is to perform a heat loss calculation for the space, then match the heating capacity of the system to the heating demand of the space. Makes sense, no?
Bathrooms can be a challenge. Depending upon the layout, bathroom floors can often be less than 50% of the actual space (due to tubs, toilets, cabinetry, etc. taking up floor space).
Hydronic systems are more expensive than electric systems to install and are generally not a good option for a single room - there needs to be a boiler of some sort, plus a means to distribute that warmed water to the room. Electric systems generate the heat right in the space and doesn't take up additional space for a boiler.
As to "green" - define "green". Electric radiant heat, by definition, is 100% efficient. If the source of the electricity is renewable, such as hydro, solar or wind, that energy source is much "greener" than a boiler burning gas or oil.
As for the "hydronic is cheap" comment - yes, it can be less expensive to operate than hot air systems simply because it is a radiant system and radiant systems are generally going to be more energy efficient than hot air systems. But if you want some hard facts, I invite you to visit my page where I describe two buildings of the same type - one uses electric radiant heat, the other uses hydronic radiant heat. The electric radiant heat system used 50% less energy than the hydronic system.