I'm trying to make a web app that will manage my Mercurial repositories for me.
I want it so that when I tell it to load repository X:

Connect to a MySQL server and make sure X exists.
Check if the user is allowed to access the repository.
If above is true, get the location of X from a mysql server.
Run a hgweb cgi script (python) containing the path of the repository.

Here is the problem, I want to: take the hgweb script, modify it, and run it.
But I do not want to: take the hgweb script, modify it, write it to a file and redirect there.
I am using Apache to run the httpd process.
As far as you question, no, you're not likely to get php to execute a modified script without writing it somewhere, whether that's a file on the disk, a virtual file mapped to ram, or something similar.
It sounds like you might be trying to pound a railroad spike with a twig. If you're to the point where you're filtering access based on user permissions stored in MySQL, have you looked at existing HG solutions to make sure there isn't something more applicable than hgweb? It's really built for doing exactly one thing well, and this is a fair bit beyond it's normal realm.
I might suggest looking into apache's native authentication as a more convenient method for controlling access to repositories, then just serve the repo without modifying the script.
How can I execute CGI files from PHP?