Boiling and mashing with RIMS?

This is my first post and I've tried looking everywhere but can not seem to find what I'm looking for. I currently brew partial boil extract batches due to space limitations and due to being in an apartment i can not use a propane burner for full volume boils. I am currently using a glass top stove and having to split the pot between 2 burners to maintain a boil. Is it possible to build a mash ton with a 5 gallon cooler and a quick disconnect fitting attached to a ball valve on the front and hook it up to a RIMS system, then transfer the quick disconnect to the brew kettle with a quick disconnect and ball valve and use the Rims to assist in bringing the full volume of wort to a boil. Of course I would have some sort of temp controller to help control the temp of mash but ramp it to full heat to help with the boil. If anyone has tried this let me know how it works and make any suggestions. Also would I have to worry about scorching the wort if I did this?

You would be better served with a heatstick to help boiling.