Yes, if the question is precisely, "Are relationships the single most determinant factor in winning jobs?" Since so far at least the only other contender for most important factor is technical fit/superiority, let's simply ask, which has the greater likelihood of success?
1. Good product and Great relationship
2. Great product and Good relationship
In my experience number one wins > 75%.
One reason is because from the perspective of the decision maker, the assessment of the relationship is one that they themselves determine, i.e. 'I like Bob, he's down to earth like me, and not a bullshitter. If there is a problem later, I feel like I could say WTF Bob? if I needed to..."
The better product/solution for the job though, is more subjective, and far more dependent on external evaluation of contradictory information.
Since both pitchmen are saying they have a Great Product, unless the deficiencies of the one product are glaring, you will believe the one that you trust more, usually the one you have a better relationship with.
Also, it should be pointed out that although the person with the Great relationship can get undeserved work by using the standard 'full-court press' after 'pulling out all the stops', this will lead to the loss of relationships and therefore is ill-advised... Unless the job is really, really big!