GPS hardly draws any current, nothing to even worry about.
Heated grips, heated clothing, high wattage lighting are what use lots of power.
Can't tell you much about the charging system but I use a GPS on long trips on mine no problem. 16,000 miles on the original battery on my '07.
What type of set-up off the battery are you using? The only ones I`ve seen are by Powerlet or NewBonneville.