No, cut your strings. Most strings have a hex core, so the wraps stick to it. Some have a round core, so you need to bend the string before you cut it. If they have silk ends you don't have to worry about it.
Here's how I sting up basses. I install a lot of strings every month, so after a while you get good at it!
I put the string into the bridge, and pull it up to its tuner. I then go the length of 2 tuners past the tuner you are going to wind onto, and cut the string there. Most bass tuners have a hole for the end of the string, so I stick the end in there, and then start winding the tuner so that as you add wraps, the end of the string you are holding is down towards the headstock. Your wraps should not over lap, and you only want 2 or 3 wraps around the post.
You cab hold the string down with the hand not winding, against the fingerboard. I press it down with my index finger and use the others to pull it up to keep it taught.
After the string is on, and up to pitch, grab it around the midpoint of the string, and pull it gently up about an inch. It will probably need to be tuned up again, and then repeat that. That gentle stretch pulls the wraps on the tuners tight, and the string wont slip out of tune now. Otherwise they will detune for a day or so.