My hunch is that the people codifying spelling rules for Polish (in the 18th century, I guess) all spoke German and knew that "v" stands for f in German, and thought it was "occupied". This is of course just a guess, and is weakend by all the other non-standard solutions in the Polish alphabet. But I am not Polish, and my Polish friends could not answer either. PS: I really hope that this would qualify as a history question - as I have been looking for the answer for many years - and very much hope to find it here :)
You could try asking at /r/linguistics as well.
XIII century- Księga Henrykowska
"Day ut ia pobrusa a ti poziwai"
this is first known fully written polish sentence, it contains 'w'. Pronouncing of letters like 'y','u', 'i' and others is differnet now. But 'w' is the same, and it is like english 'v' in 'very' word.
so your theory is not possible.
polish w you read as english v (very) and polish ł as w (where)
so there was no need for v in polish alphabet
btw sentence above was said by a baker to his wife and this loosely translates to 'leave it, i will do the work, you should rest'