Yes, it should work, but if your goal is for it to provide Internet access then some configuration changes will be required. You will basically want to configure both routers for a roaming network.
I have a router (non apple) somewhere in my house and an ethernet cable that goes all the way to a point in the house where there is no wireless reception. If i connect an airport express to that cable, will it work as a "new" wireless connection without any major configuration?
Thanks for reading and helping!
Possibly. Since most of the settings for the roaming network is done on the extending router, you could use the AirPort Utility on your iPad to configure your AirPort Express per the instructions.