Have not attempted to math it out, but some rocket first stages can make orbit alone. The difficulty is that they have a payload of zero when doing so, because they are taking all the empty tank mass and un-needed engines all the way to orbit as a single stage. Dumping mass on the way up improves mass fraction of the parts left trying to make orbit.
This is why all currently flying rockets have multiple stages.
As you note, there is a hypothetical situation if you wanted a really large empty storage tank, that a first stage body would be an option to do that by dumping engines on the way up as fuel burns off to make a one point five stage rocket.
This of course still presumes that a large metal body contaminated with propellants is useful for the final purpose (noting that in LEO reboost is required, so heavy things are still not 'free'). In many cases it may be easier and cheaper long term to use the rocket conventionally to loft a purpose designed balloon structure.
Certainly trying to move a tank structure strong enough to stand up on the pad by itself to the moon or mars is not the most efficient option, since it will be much stronger than needed for the job forcing you to burn more fuel to move it than a purpose built solution would. The other payload that this would deliver to orbit would be lots of engines, but it is hard to visualize a use for lots of sealevel methalox engines, where you could instead use that same superheavy re-useably to launch starships and pull the vacuum engines off them three at a time before sending them home for a more useful result.
