The Access2Mysql program will only convert the database tables.
As for the scripting, you would have to connect it to the mysql database. As far as db connections go, it's one of the easiest.
You can find a server that will host an Access database, but IMO those are rather cumbersome, and usually quite expensive.
MYSql is a database server, and it's geared towards multiple users. I've seen too many NT/2000 servers lag and give problems, but again that's my opinion.
There would be a bit of work involved to convert the code to connect to the mysql database, but if you choose to do it, you only have to do it once
The program you're using may have sql provisions.