In short, for archaic forms, probably not, but if you do you might appreciate some older English texts (particularly the King James Bible or Shakespeare etc) more for having done so.
There are exceptions where the archaic word holds over in the form of an idiom or quotation, for example:
Manners maketh man
Note that most native English speakers don't understand old and archaic English words, and hence you probably should concentrate on becoming good at modern English first.
You should, however, be aware that occasionally (particularly on television and in marketing) modern native English speakers will misuse old English by adding "-eth" to verbs and sprinkling the sentence with words like "thou" and "ye olde" in order to make their sentence sound "medieval" or "authentic".
Often these fake medieval constructions are utterly ungrammatical in modern and old English ("Cometh to our garage and buyeth a new car! Half price for thou in our ye olde themed auto-sale!").
Consequently you'll probably find that if you do learn these old forms, you'll find very little modern use for it, and it'll make it all the more jarring when you hear such grammatical abominations on TV or in adverts.