Running the numbers for using Super Heavy as an expendable SSTO, it would be capable of putting about 25 tons into LEO. (Simply add the proposed payload to the vehicle final mass until the MR drops to the mass ratio needed, about 13.69.) So, with a fairing, some solar panels, and drop a few engines…doable, but with all the caveats outlined above.
A couple other observations…first, if you’re going to put a Super Heavy on orbit, then you have a really big propellant tank, but a bunch of sea level Raptors. Same problem with just using the 3-engine gimballed core for a Starship-like intermediate stage. If we’re serious about giving an extra kick to deep space missions, a mission-specific design seems more logical. On the other hand, every specialized design requires a whole lot of work. It’s at least plausible that SpaceX might conclude that a sub-optimal design is “good enough,” and avoids all the work needed to design, fabricate, and test a specialty intermediate stage.