Perhaps you know this already but ござんす is very probably from ござります (り > ん is a common sound change, and I guess ま just devoiced and then dropped, but I could be wrong) and listed as such in dictionaries. Actually, there appears to have been many variations on ござります, including ござんす but also ござりす, ござりんす, ございす, ござます … basically every permutation can be found if you look carefully enough, although I think ござんす was one of the more popular ones, and has retained some popularity as a present-day “old speak” type of thing.
In terms of period, Nihon Kokugo Daijiten indicates rising popularity in late 17th and early 18th century, so definitely Edo era. In linguistics terms, this is considered modern Japanese already, but I guess for us it seems like long ago. 
If you ask me, what betrays that is the use of ます (ござる+ます), which came to be used at the beginning of the modern period (17th century onwards). So the info seems to match. So yes, many samurais around, since it would be during the Tokugawa shogunate… but samurais at peace (in late 17th century), if that matters!