That would be my preference, unless you know for certain the probe can be kept submerged for years at a time.
I have mine taped/strapped to the bottom third of the fullest keg, under a 4x4" patch of 1/4-3/8" dense packing foam.
What controller do you use?
Have you set enough temp difference between the on and off trigger temp?
To help save it from burning out prematurely, definitely set the compressor delay to the maximum possible. IMO, the 10 minute "standard" is too short, I'd prefer at least 20-30', maybe even 40-60' for larger fridges/freezers. Although you could extend that interval by selecting a somewhat wider low/high interval.
Aside from filling that hole with some insulation foam, I'd insulate those beer lines going to your faucets. That might improve your pours too, especially the "first" ones. Bundle them of course, then insulate the bundle.
Although "heat/cold draw" maybe minimal from them, I'd probably insulate the gas lines, too.
On another note, there are better beer/gas lines available now (EVA Barrier), being much more oxygen impermeable than vinyl.