Yes, most of the usual Solar converters work with a "Stop / Start" behaviour, based in the battery state, as it is done in PVsyst.
Some sophisticated converters use indeed a more complex charging strategy: when the battery is full (i.e. attains the charging OFF threshold), they don't cut, but reduce the voltage appplied to the battery, and maintain it at a value ensuring a little current (floating mode).
This has not yet been implemented in the simulation of PVsyst, it should be done soon.
This mode could indeed be used for ensuring your proposition, which is to maintain the PV production when it is sufficient for covering the user's needs. This will require a special operating mode of the controller, which is to exactly adjust the output power for ensuring this floating voltage. In the same way as when limiting the output power of grid inverters, this will be obtained by displacing the operating point on the I/V curve.
However if your battery is sufficiently sized (2-3 days of consumption), as far as you don't have to cut the load because it is discharged, the balance of the unused energy will be exactly the same. Because the Solar PV system cannot produce more energy than the user's needs !
If the battery remains charged during what would otherwise be the "battery cut", it will not need to be charged afterwards.
The only difference will be the battery wear due to cycling , and eventual battery efficiency losses.
You could indeed observe a (very small) advantage if you have to cut the user due to a complete discharge of the battery.