Temporarily? Sure. Long term, I wouldn't mess with anything short of a whole new run, or a solder and shrink wrap job. Tape WILL come off over time. At a MINIMUM I would crimp some connectors...
Some will argue that you are going to lose signal quality because of a splice, which is true, but I am more concerned with the wires not just falling apart from each other and you getting zero signal.
PS. A cheap-o $10 soldering iron kit that comes with electrical solder will work just fine. Grab a couple bucks worth of heat shrink and be done with it.
