Absolutely it would be possible. In fact, it's pretty easy.
You can install either 400-series or 700-series LED modules into the Edge frame, depending on your taste. Either series is the correct height to fit. Steady-burn modules are easier to work with in this application than SmartLED modules.
If your current bar is an Edge 9000 where the strobe modules are held in with screws and plastic retainers, then you will probably want to purchase several lighthead mounting clips, like these:
http://cgi.ebay.com/292187363590 That eBay seller is also a member here, by the same name. Using these will simplify installation and any future maintenance.
You will need some kind of LED flasher to flash the LED modules. Something like a ULF44 would be suitable, as it can handle 5 amps per channel across 4 channels, for 20 amps total. You could replace the Edge control board with a Freedom (or Liberty) control board, depending on your needs.
If you have an Edge 9000 or Edge 9M frame, you will need to make a decision about the length of Freedom corner modules you install. Standard (short) Freedom corner modules will fit without issue. Extended Freedom corner modules will fit, but they will take up half of the alley light position, and they will require the removal of one of their mounting tabs with a razor knife. Look here for details:
https://elightbars.org/forums/threads/whelen-edge-9m-questions.35474/#post-326242
If you have an Edge Ultra frame, which is deeper front-to-back than the Edge 9000 or Edge 9M frame, then you wouldn't have to worry about modifying the Extended Freedom corners. The frame extrusion is large enough to accommodate them, plus LR11 alley lights.