There is no way to say 100% that it won't give you a problem... Most likely it won't. That wavy condition is a result of the delamination of the filon (the white external portion) from the luan backing (the structural underlayment portion). This does weaken the outer covering of your trailer and looks pretty bad. Aside from the looks, the resulting structure is weaker than the bonded original and will result in more flex which can result in more leaks as the flexing weakens the seal.
Most units have additional "clamping" along the edges of their attachment points to help keep the trailer in one piece...structurally it should be sound enough to make the trip. It may or may not develop more leak points along those seams, but, the worst of the damage is already done. I would make sure that the seams have been re-caulked and I would check those repairs religiously while traveling, but, I, personally wouldn't cancel a pre-planned trip that was of short duration. I wouldn't go on the road for several months, though, without having the unit gone over professionally to make sure that further water incursion wouldn't occur or that structural integrity wasn't affected. There are many trailers that have delamination areas and once resealed they are still quite usable, however, delamination in certain areas can lead to both internal and external structural problems if not rectified and you also have the likelihood of mold and mildew issues inside the wall and some people are sensitive to either or both and neither is good for your health even if you aren't sensitive.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)