Yes you can leave it hooked up. You also need a supply of 30 amp slo-blo fuses for the inline jack fuse. My Barker would sometimes blow the fuse. Be careful to not reverse the jack direction without letting it come to a complete stop. I think that caused the fuse to blow several times. Also, if you run the jack up or down to the end of the travel and the clutch slips, back it off in the opposite direction a bit. I had mine jamb in the up position. A Barker rep gave me that advice. They did send me a new post to solve the problem. I don't know if the newer ones have that issue, mine was new in about 2006.
2014 Eagle Premier 361REQS
2013 Ford F350 Crew w/ 6.7 diesel