Yes you can use that right next to your current bulb to provide extra heat. But really you do need a way to measure the temps. You don't want to make it too hot just as you don't want it to be too cold. It's a fine balancing act but once you find the bulb that works for you, you're set.
What I personally would do until you get your thermometer, is move the one you have currently to the cool side and keep it there. Set up your che and bulb over the basking spot. That SHOULD provide a decent amount of heat, how much we won't know. Now if he has enough of a basking area and it does happen to be too hot, at least he can sit somewhere where the temp is where he likes it.
The reason for moving that thermometer to the cool side is this. If you add the CHE and it does end up making things too hot in the tank, you don't want to overheat your beardie. Keeping the thermometer (while still semi-inaccurate) on the cool side will at least give you a ball park estimate of the cool sides temp. If the cool side is getting too hot, you will need to stop using the CHE. If cool spot stays ok, then we know that if the basking area is too hot, your dragon can go to the cool side to cool off. Those analog thermometers seem to be more accurate at lower temperatures just to mention.
-Brandon