My answer is "yes", because it' s easier and cheaper than ASI, for instance(FMI and ASI are the only historical registers recognised by law, at the moment).
The procedure to get a vespa registered is not difficult: you can get any information HERE, on the official website of FMI. But you have to wait for a little while because, due to a new law just come out, FMI is updating the forms to fill and something in the procedure to follow.
Anyway, should you have problems understanding italian, ask for help
