I get asked this question quite often and the answer is almost always a resounding, yes. There are always caveats to everything however..
Last summer I finally had the opportunity to set this up for demonstration with a small 12W panel and two battery banks. It then took me 9 months to get this article up on my site.. Sheesh, sorry for slacking...
Both banks were charged with the 12W panel and a Morningstar PWM solar controller until they were full. The controller was then removed and the panel allowed to feed the banks unregulated.. The panel was left flat, not angled towards the sun, just like it would be on a boat. Getting these banks full did not happen over night because I purposely drew them down to approx 60% SOC. With the solar controller removed the small 12W panel eventually brought both banks over 15V!!! This panel is 10% of the 125Ah bank, in wattage, and only 5.5% of the 220Ah bank, in wattage..
Bank #1 = 220Ah Lifeline 6V AGM
Bank #2 = 125 Ah Marine Maxx Group 31 Flooded Lead Acid
Solar Panel = 12W
As you can see even a diminutive 12W solar panel can push a 220Ah bank of Lifeline batteries well over 15 volts!!!! Do you need a solar controller? The answer is almost always a resounding YES!