To answer the OP's thread title question; yes no problem.
Modern battery chemistries allow higher charge voltages than in the past when it was generally accepted 13.8-14.2V was the charging range but up to 14.5V is considered safe these days.
As you've seen a fall then a slight rise in the current drawn IMO this indicates the battery is taking a charge and will likely give more service. However 6 months idle for a LA auto battery is downright abuse and some steps can be taken to reverse some of the plate sulphation that has taken place.
When the current draw has fallen to a couple of hundred mA remove any cell caps and proceed with an Equalisation charge as dieseltech82 has described, checking electrolyte levels are maintained with distilled or rain water or better still some new electrolyte.
Cycling the battery with a gentile discharge and recharge a couple of times can help recover tired batteries and you'll get a feel for when it's charged from the charge current falling off.(CV)
Good luck as you don't get them all back.