I'm not an expert so I don't know whether the panel would be damaged when the mains charger is on. However, you do really need a controller unless the panel is a small one, to prevent overcharging and to prevent power "leaking" during darkness.
The C&CC publishes general notes
Here.
"Larger solar panels can over-charge your battery
unless you add a regulator into the circuit, to restrict the current to a
sensible level.
As a rule of thumb, check whether you need a
regulator by taking the rating of your battery in amp hours (Ah) and
dividing by ten. If the power (in watts) of your panel is lower than
this figure you won’t need a regulator. If it’s higher, you will. So for
a 90Ah battery, a panel of 9W or less won’t need a regulator. Anything
more than 9W should have one. In real terms, therefore, most solar
panels for leisure batteries will need a regulator. Many kits sold for
caravans and motorhomes will have one included.
When it’s dark, energy can flow from your battery
back into the solar panel so there would normally be a diode in the
circuit to stop this happening.
A charge controller will normally include both a
regulator and the appropriate diodes to protect your battery, though the
terms ‘regulator’ and ‘charge controller’ are not always defined in the
same way, so it’s worth checking exactly what is included in any kit
you are looking to buy."
Graham
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