Hosting PHP API with MySQL for mobile app in google App Engine. How? Good or Bad?

You ask:

I wanted to know if its possible to host just plain old simple PHP scripts on google app engine. This scripts will just be bridge/api between MySQL(planning to use cloud SQL) and android application.

Sure! Unless you're doing very fancy stuff and running afoul of the "sandbox" limitations explained at https://cloud.google.com/appengine/docs/php/#PHP_The_sandbox, your PHP should run fine on App Engine.

If its possible than i would like to know if is it worth it? How its better than hosting scripts on regular web host?

If you don't plan to take any advantage of the differences of App Engine and Cloud SQL -- you're adamant to use them just as if they were "regular web [[and MySQL]] hosts", with zero interest in actually taking any of the advantages -- there may still be wins, but, only in somewhat unlikely circumstances.

For example, you might respond to a sudden spike of traffic much better with app engine's autoscaling -- but if your attitude to serving your customers is that you can't be bothered to do a tiny amount of effort to customize your code to your actual hosting platform, then I'm not creative enough to figure up a scenario in which you would get a burst of traffic; rather I would expect your more sensible competitors, happy to spend a couple hours learning and another couple hours adapting their code and config, to eat your lunch (and breakfast and dinner -- elevenses too, probably) and take away your customers so you'll never have to worry about traffic bursts and scaling up to larger volumes, as your volumes, I would guess, will not get any larger... on the contrary.

As Jerry Pournelle would put it (and did, in "Oath of Fealty" -- by far not his best work otherwise) -- "think of it as evolution in action".

Ah well, I already loved Jerry as a writer 12 years ago -- then, see http://code.activestate.com/lists/python-list/335605/ , in his column on "Byte" (a magazine I also long loved, and never failed to devour cover to cover, every month! for ages), he splurged love upon Python... and specifically upon my own book, "Python in a Nutshell".

I didn't make any substantial amount of money directly out of the book, but (together with the Python Cookbook) it did help ease me into many great consultant contracts, and later led me to the Google job I still have and enthuse about. (not to mention my marriage -- http://www.aleax.it/marall1.pdf !-).

So I'm biased and can't stop loving Jerry -- and his "evolution in action" is part of the package...!-)