Furling jibs
As you know, jibs for furlers have a luff tape along their luffs in place of a bolt rope and hanks.In my opinion, the most common luff tape size is no. 6 which is approximately 3/16 inch diameter.I seriously doubt the bolt rope on your jib is 3/16 inch diameter, most likely much larger, and therefore too large to go into the groove of the furler.However, you just might have a wire for the bolt rope, but that too I think will be too large for the furler. Further, even if such wire were say 1/8 inch diameter, you may need to eliminate the eye in the wire at the head of the sail and sew on a tape at the top to use as a head cringle. I personally think this is not a wise procedure as the wire in the luff will then be loose in the luff and the jib will not set properly in the groove.Hence, the answer for your first question is most likely no you cannot use your existing jib on a furler without at least installing a luff tape.Now for the foam luff.As one furls a jib to a smaller size, the foot (primarily) and the leech tighten up at a faster rate than the middle body of the sail. This means that the middle body of the sail fills too much and it is difficult to reduce power. Hence, by adding a foam strip to the luff, the middle body of the jib tightens at a rate more similar to that of the foot and the leech and a flatter sail is achieved which is better for reducing power.There are differing opinions about the importance and effectiveness of having a foam luff, much of which is dependent upon the size of the furling headsail (150%, 135%, 110%, etc.), the particular needs and sailing style of the sailor, and the size of the vessel. So as such would apply to you, this would be best answered by those with a vessel similar to your own, a headsail of your size, and sailing style and requirements similar to your own.As for installing a furler while the mast is up, such action is more than likely going on right now as you read this by some other sailor in a fashion identical to the one you described.