LK .. a few personal opinions ....
The suck/blow effect of LGV's is not stopped by fitting a stabiliser, but... if an inexperienced tower were to "over-react" (oversteer) to correct this, a stabiliser would lessen the pendulum effect on the 'van and possibly prevent a snake happening.
Same applies to gusty crosswinds, adverse cambers, swerving for animals/pedestrians/other vehicles etc etc etc
Once a snake starts - and an experienced tower will do all he/she can to prevent such a thing arising - a stabilser can ASSIST in the recovery, again by reducing the pendulum effect.
I would always advise an inexperience tower to use one, as the chances of "getting it wrong" are greater with less experience.... however I would never tow without one now - with 20 years experience - as I know I can make mistakes, and sometimes I have to react to the "mistakes (?) (bad driving ?) of other road users, these circumstances can set up an incipient snake ... a stabiliser will then ASSIST in recovery.
A stabiliser will not make an unsafe van safe, it just makes a safe one a little more safe