If you remove the showerhead, you'll have unrestricted flow, and it would be similar to trying to fill the tub. The only way to measure the flow of a showerhead is with it attached. The manufacturers do that for you, and the info should be available as part of their specs. Federal regulations (in the USA) restrict a single showerhead to 2.5gpm maximum. Most use somewhat less. This is at some reference water pressure, and if your pressure differs, it will flow more or less. Many manufacturers use a restrictor (some can be easily removed) to limit the flow to meet the regulations of a showerhead.
A typical valve can flow in the order of 6-8gpm if it is fed with 1/2" lines, and maybe as much as 13-15gpm if using 3/4" lines (the largest shower valve you'll find easily).