Am I crazy to try to refinish this $99 set of (probably) fake Tulip chairs?  

The arm shells
Are drilled in a different place in the front though... presumably to accommodate the tulip style bases (which covered up the HM logo).

Regarding the drilling
Armchairs: the bases are attached with bolts that have been drilled through. I have seen other pics of HM chairs like this with the same bolts. What you're saying about them being previously upholstered seems logical
Sidechairs: the bases are attached at the bottom but not via drill holes. There are 3 additional drill holes that are the mystery holes. My guess was that these were from previously attached upholstery too.
Well, for now I'm going to keep cleaning them up and see how nice the shells turn out. Inside or outside chairs, I still like them 🙂
p.s. Thank you to all of you - its great to have so many responses!

I have the answers you need
Well firstly the arm chairs are eames ,and someone very creative put them on a saarinen base.As far as the side chairs they are canadian knock offs how do I know I have had to many.I recommend bleach this will clean well the fibers.As far as the bases very smooth sand paper a lot of sanding ,and them primer ,and paint these are very tricky to repaint , but with much patience anything is possible.There will be no other feeling of satisfaction once the set is finished, and then it will be really yours, and you probably will appreciate it more. Craigslist has had many good deals, and happy hunting.

Canadian indeed!
Thanks - it would make complete sense that they are Canadian knockoffs since I am up here in Canada.
Yes, you are right about making them "my own". I am having fun and can't wait to finish them and share pics with everyone here.

Some progress shots...
I picked up 2 more armless chairs for $60 off of Kijiji (like Craigslist). This time they had upholstered seats still. This is great because I'm going to use the old seats as a pattern to make new seats.
Here are some pics of the new chair and my progress on the other bases.