If the Gun is emplaced, as long as you record the fact it has WA as well, it will retain WA until such a time as you may want to decline WA or move the gun (both probably unlikely). If the gun is not emplaced (very seldom & highly unlikely) in the situation it's presented (in OG) it will automatically have WA with no need to record it. So yes, in most instances you will be able to have a LOS over & beyond the hedge/wall.
Small correction to be complete, if in a Trench, the gun would only be able to see adjacent hexes if the LOS crosses a hedge/wall. So, very limited LOS, but can still see adjacent hexes across walls/hedges (and ignoring Bocage, LOS doesn't depend on wall advantage as was pointed out).
One of the times a unit can claim WA is when is when losing HIP status. So I don't think it needs to be recorded. Also here is some Perry Sez Q & A related to this.
Can a gun be Emplaced in a hex with a wall or hedge hexside? A. Of course, and Emplacement has no affect on claiming WA, and claiming WA does not supersede the Emplacement TEM.
Assuming a gun can be Emplaced in a hex with a wall or hedge hexside. Must it claim WA instead of its Emplacement modifier (+2) when an enemy unit becomes adjacent? Must it claim WA instead of its emplacement modifier (+2) if it has at least a +1 TEM (EX. woods) when an enemy unit becomes adjacent? A. An Emplaced Gun in OG, etc., must claim WA (just like everyone else) and one in +1 TEM, etc., need not claim WA (just like everyone else). However, “when an enemy unit becomes adjacent” is not normally one of the times you can claim WA (unless you are losing HIP).
If an emplaced gun does claim WA does it receive its +2 Emplacement modifier vs units that are not adjacent? A. It may claim +2 Emplacement TEM vs all units as usual.
Though if you are behind a Bocage hexside you probably do want to record it as otherwise you won't have a LOS past the adjacent hex.
Note that in rule B9.324 the last sentence:
"..A hidden unit can never claim WA and must be placed (concealed) onboard to be able to claim WA during play, but may do so at any time—even at the moment an enemy unit moves adjacent and wants to claim WA."
was replaced via errata in ASL Journal 8 to this:
"...A HIP unit that desires to claim WA during setup must secretly record such WA status [EXC: 9.323]. A HIP unit may forfeit WA (even if it had been mandatory) to an enemy unit claiming WA (even implicitly; 9.323) over a shared hexside and remain hidden but must be placed on board (concealed) to deny an enemy unit from claiming WA, or to claim WA that is not mandatory and was not recorded, or to forfeit WA if no enemy is claiming it. Hidden units are not considered when determining if broken/unarmed units may claim WA (9.32)."