Ed -
The answer is: Sort Of!
If you are referring to EFIS systems, most of them do not actually contain a radio or a transponder *inside* the main system. However, both MGL and Dynon units can easily integrate with a reasonable assortment of radios & transponders, allowing you to operate them via the EFIS unit.
For example, my MGL iEFIS Discovery Lite controls my Trig Mode-S transponder (which will be ADS-B compliant when I add the certified GPS in a year or two), and it also controls my MGL radio. For safety/redundancy, I still mounted my radio in the panel (so I can control it if the EFIS has a problem); but the Transponder is in the baggage area and has no panel-mounted controls other than the EFIS.
Dynon gear works very similarly, and although they might not have quite the same budget price-point as MGL their equipment is very very nice (I live near Dynon HQ and know folks there). There's a bit more "polish" put into their stuff - for example, I had some RFI issues with my MGL EFIS and in talking with my Dynon acquaintance he mentioned how Dynon had those issues in the beginning, but now designs and tests extensively to avoid that sort of thing.
Setting up this kind of centralized control requires ~4-6 extra wires to be run, but its not hard. There's plenty of information out there on which radios & transponders work well with each manufacturer, if you decide to head in this direction. And you can always ask questions here!
--Noel
Sonex #1339
(first flight waiting on my Turbo to be rebuilt)
P.S. Here's a photo of my panel. The main instruments you see are the Discovery Lite, an MGL ASX-1 (backup airspeed/altimeter instrument), and the V6 radio. To save panel space, the new MGL radio model can be remotely mounted (i.e. no separate control-head on the panel).
https://flic.kr/p/21TkcYs