Games on external HDD?

yes you can

USB is much slower than SATA or IDE so there could be some slowdowns.

You SSD could be DOA, it could live for a week or it could live for years. It all depends on the usage and dumb luck.

To answer your question
But why not use the secondary as another internal drive? I do that and it works perfectly.

I would recommend USB3 and I would also recommend to be patient.

Don't forget that some games save data in the My Documents > My Games directory, so it might not work as you'd like.

You can manually set up a secondary game install location in Steam.
(View > Settings > Downloads> Steam Library Folders > Add A Library Folder)
From then on, any time you go to install a game it will ask you which folder you want to install it in.

As for SSD life spans, don't worry about it. Yes, flash memory does have a limited number of writes, but that amount is so incredibly high that it's never going to be something you will need to worry about. Sure, you may end up simply getting a BAD drive, but that can be said about pretty much any electronic device/component on the market.