Alternator + solar charging has considerable benefits over alternator charging alone, and over solar alone.
Alt charging alone is unlikely to get lead-acid chemistries fully charged since Absorption can take hours. Incomplete charge (Partial State of Charge, or PSOC) over time will result in battery murder.
How to avoid (or attenuate) battery murder with this scenario:
The reason for this is related to how lead-acid banks charge; they can take a ton of current in the first ~80% of charging (Bulk) then they hit a kind of wall. At that point you could drive 100mph or hook the bank up to the Hoover Dam's electrical output and it wouldn't finish charging significantly faster.
From ~80% to 100% (Absorption stage) charging requires little current but a long time holding at a relatively high voltage. So in our alt+solar scenario the alternator does the heavy lifting in the beginning then a small solar install does the light (but lengthy) work at the end.1)
Solar power is relatively weak compared to alternator charging. Solar is most challenged in the morning when the bank is deeply discharged. The sun is weak then but the bank needs a large supply of current (early Bulk charging).
PWM controllers are especially hamstrung in this scenario; since they run the panels at battery voltage (Vbatt) they produce the least power exactly when the most power is required. By the time Valt is reached PWM controllers are able to produce meaningful power.
Alt charging shovels current into the bank up to the point that alternator voltage (Valt) is reached. Solar can take it from there. A good metaphor might be a two-stage rocket: the alternator does the heavy lifting then the solar charging takes it to high altitude.
Boosting solar charging with alternator, genny, etc, works best during bulk stage. This is true for alternators because their terminal voltage is rather low, and for both generators and alternators because Absorption stage takes little current and a great deal of time.
A bare solenoid doesn't know/care about the state of either battery, only that the ignition is in the ON position.
the chassis' electrical system can be damaged by the overvoltage. When manually equalizing ensure the systems are not connected. If your charge controller does automatic EQ try to disable that feature. You may also want to automatically disconnect alternator charging when house battery voltage rises beyond a given setpoint.