Yes and No... the issue is one of density of the medium over which you wish to travel
18 psi is 18 psi IE that is the pressure inside the tyre 'pushing' on the inside surface and the ground is pushing back with a similar pressure on the outside surface.
Yes there are other factors like sidewall stiffness etc but they are much less a factor so for the purposes of the discussion lets ignore them for the moment...
If the pressure is raised on the inside of the tyre it will 'push away' and decrease the amount of tyre surface in contact with the ground... if the pressure inside is lowered the tyre surface in contact with the ground will increase until the two forces get back in equilibrium.
Yes, the more you load a vehicle (wagon or ute, doesn't matter) the more tyre surface ends up in contact with the ground but the key is the pressure exerted per square inch has increased but the density of the sand has not so neither has its ability to support the extra pressure/weight.
The medium (sand in this case) has a certain density and will react pretty much similar to a fluid so is analogous to a boat in a way (except a boat cannot change its footpringt).
The more weight in a boat the further it sinks until equilibrium IE the deeper in the water it rides and the more power it takes to displace.
The 4WD reacts in a similar way in sand.
Lets assume the sand/mud/snow density etc will support a surface pressure of 18 psi before you sink to a point where your 4X no longer have sufficient power to proceed.
Then 18 psi is the max pressure you will be able to exert onto the surface and get through.
A tyre with say 24 psi will exert a higher surface pressure than can be supported and will bog down or mire.
Sorry for the ramble so a quick Summary maybe in order?
If two vehicles of different weight but similar power availability and drive fitted with identical tyres attempt to cross a surface the tyre pressure at which point they will succeed or fail depends on the ground pressure exerted and is independant of the actual mass of the vehicle.
If a 3 ton Patrol fails at say 24 psi but gets thru at 18 psi then a 15 ton truck will fail at 24 but get thru at 18 psi also (all other things being equal)