I have an older 2 speed Dremel and it works, but I had to make a few modifications to get it to cut accurately.
Some of the Dremel models (and others) only accept pinned blades which will really limit the types of cuts you can make.
Off the top of my head I don't recall where I bought the adapter that made using pinless blades easy to use, but when I find it I'll post it here. The adapter didn't cost much more than a few bucks and it was worth more than the purchase price.
If you go with a Dremel or other less expensive brand just be sure to buy good quality blades..
Personally I like the Flying Dutchman brand and they're not that expensive.
You'll probably break several before you figure out how to set the blade tension. The bad news is the better blades break easy. The good news is once you get the tensioning down pat you won't break them as often.
Edit: Well that was easy.. I watched the video then purchased the adapter he talks about. There's a link to the place that sells them.. Nice, cheap adapter and only takes a few minutes to install..
The Dremel is a similar setup to the HF saw..
Something else..most of the blowers on these saws are crap so you might want to invest in an aquarium air pump to keep sawdust off your work piece.. They're cheap and effective.
One other thing..I sometimes buy thin, 1/4" or thinner boards from the ebay seller csmdeals88 .. They're all nice and flat and relatively inexpensive..