Just my personal thought:
My opinion of factory rifle bedding is so low, that I wouldn't even consider shooting such a rifle before having it bedded by someone I considered competent.
Why???
If it is a real sporting rifle, I want it to shoot excelently with some or all of the premium brands of commercial ammo availible. Experimenting with this expensive ammo can actually cost more than the bedding job itself. When the rifle refuses to shoot well with any of this expensive stuff, the first thing to suspect is the bedding. So then you have to pay for the bedding job and then reshoot all the expensive ammo again. You might just as well have had the job done right at the beginning. As often as not, I suspect you will save money, break even in the long run and have more confidence in the arm.
If someone out there knows how to eliminate bedding as a prime cause of a rifle's lack of accuracy without firing the gun, I would like to know about it.
I suppose if it shoots well (don't know how to quantify this) with cheap ammo, I guess that would give one the confidence to consider the uncorrected bedding as O.K. But if it doesn't shoot well with this stuff, you don't know if it is the rifle or the ammo.
If you reload for the cartridge in question, then you might load up something like Sierra's recommended accuracy loads with Match King bullets as a good and relatively cheap test, but if the cartidge is new for you, you have to buy dies, which only makes sense if you want to shoot this cartidge a whole lot. If you don't reload or don't really want to get involved in reloading, this option is either epensive in the short run or out entirely.
This just my opinion, it is certainly not proven by scientific experiment.
As for synthetic stocks, I don't own a single one, so I don't know if their bedding problems are as bad right out of the box as is common with wood stocks.