Hello and Welcome!
Beardies are generally very solitary and territorial by nature. So, in answer to your question, yes... they will fight over space, food, basking spots, etc...
Beardies can actually get pretty aggressive towards one another. You don't want them fighting. This could end in serious injury, such as missing digits, limbs and even death unfortunately.
Even if there is no fighting, there can be dominance issues which can lead to overstressed beardies and one or more not thriving properly.
It is best if you can get them all their own enclosures. The size set up you have right now is what is recommended for One beardie.
Getting them all their own enclosures will guarantee them having happy, healthy, stress-free lives.