"On the fly" is often taken to mean downloading spatial data from a source as you travel. For example, Google Maps tiles via your cellphone dataplan as you drive into a new city. The point of that being, you won't be getting anything "on the fly" if you're outside of the coverage of your data provider due to mountains or anything else that masks signal transmission. You will have to find out from any provider whose mapping products you're interested in if your GPS will download map files on the fly, and if they make those map files available for download on the fly.
I do professional work as well as recreational use of GPS units. There is quite a wide variety of products out there, both from the dedicated manufacturers of GPS units i.e. Garmin, and then the quickly increasing field of apps for cellphones. A lot of people have decided that they prefer using their smartphone/tablet for travel instead of a dedicated GPS; that's a decision you have to make. So, dedicated GPS unit (like you're talking about) or smartphone, you'll have to inquire with your manufacturer or view the available apps to determine if their product allows you to view raster data (orthophotos or satellite imagery) overlaid with vector data (topo data). I can't point you at anything because I haven't been looking at these products.
I still prefer dedicated GPS units, but I have the advantage of not only having access to recreational GPS units like the Garmin Rino, but professional units (with professional mapping capabilities) of units like the Trimble Juno. Having said that, I have started riding new country/multi day rides with a 7" Samsung Tab 2 loaded with the DualSportMaps app in the map pocket of my WRR's tank bag - that app allows you to preload topo maps, satellite imagery, orthophotos, etc before leaving the house. With the tablet, I can stop, and in a few seconds have the tablet out and be exploring what's nearby, where a road might lead, etc. You can do that on a GPS or smartphone as well, but there's a big difference between scrolling around in a tiny screen and scrolling around on a big screen. Enormous difference.
After using one, if I was heading out on a really serious adventure ride, I would be taking a small 7 or 8" notebook or tablet along. Something that could run Basecamp/Mapsource at the end of the day to preview/edit/ create tracks, stop and explore nearby areas via imagery and topo files, etc. You can do that with a GPS or a smartphone I suppose, but I think that is just too damned painful. Android devices like my Tab 2 won't run Basecamp/Mapsource, so I'd be looking at something like a Lenovo Miix 2 or similar that can run Basecamp/Mapsource.
I will offer you my opinion that I haven't found much use for combining raster mapping and vector mapping at the same time on professional GPS units, and I don't miss not having it on the tablet app I use. That has been available on professional GPS units since about 2004; when it first became available, I put raster and vector mapping for a work area together all the time. I quickly decided that all I ended up with was a really cluttered screen, and I ended up dumping the raster data and just sticking with the vector topo data. The problem was even worse when on the move in a vehicle. With a tablet (and presumably recreational GPS units), it only takes a few seconds to switch the mapping on display from your topo mapset files to your imagery mapset files. Your opinion, of course, may be quite different.