What year/brand/model converter do you have?
13.6 to 13.8 is normal charge mode. If it never drops down to the 13.25 volt area (float mode) once fully charged, then yes you can and will over charge the battery and in doing so boil off excess electrolyte.
Your converter may take a long time to recharge the battery. Long time can be 1 to 2 days pending how big a battery and how drained it was. But after that it should be dropping down to 13.25 float mode unless your using more battery power again. If after 3 days it is still on 13.6, then you should manually stop the charging.
And yes a battery minder that has desulfate mode on it will keep the battery maintained, desulfated and at 100% state of charge when not in use. I have used this brand with good success.
BatteryMINDer® Plus 12 Volt 1.33 Amp Charger-Maintainer-Conditioner (Desulfator) | All | Battery Chargers by BatteryMINDers.com
Searching for them on the web you can get that model for about $40.
Hope this helps
PS Just make sure you do not run the Battery Minder on the battery at the same time the converter is on. It is one or the other, not both.
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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