Yes, you're probably still going to run rich even with a high flow filter. All that smoke is generally a sign that you're getting too much fuel in your air/fuel mixture. You're getting all that extra fuel because the hole in your jet (which determines how much fuel leaves your carburetor) is a lot larger than it's supposed to be.
Please please please just buy some jets. They're really cheap. They don't take up a lot of space. They don't piddle on the carpet. Jets are your friends. You can get Bing jets from Treats. Also, the really cool thing about jets is that you can easily tune your moped because you will always know what size you've got in there and which sizes are bigger or smaller. Unless you're really anal about keeping them straight, you will have no such advantage if you drill them out.
If you want to go faster, buy a range of jets in sizes larger than the one you've got (the one you drilled out -- you probably should just chuck that one once you get new ones.) For example, if you had a 60 jet in there, get a 62, 64, 66, maybe even a 68. Buy a high-flow air filter. These are not particularly expensive either. Then put on the air filter and put on a jet that you KNOW will cause your moped to run too rich. Once you've verified that it is indeed way too rich by running a plug chop, downjet a size. Repeat plug chop. Keep doing this until your plugs are no longer black but rather a nice coffee-ish color. You can read up about all of this in the wiki, either in the Moped Jargon category or the Performance Tuning category.
If you REALLY want to go faster, you should buy a performance exhaust, but those are significantly more expensive. You can also read the article about de-restricting a Puch Maxi (it's in the Puch category) -- that will likely help your speed too. I'd still start with the air filter and larger jets if I were you. They're a good jumping-off point.