At least as the data appears today, the DOB of William Gage is 9-10 months before Daniel Gage's marriage. That doesn't mean the relationship is wrong, but it does make it slightly less likely.
As to your question at hand: DNA certainly *could* be useful to prove this connection. However, because you'd be dealing with more distant relationships, you'd have to triangulate three known ancestors with verifiable paper trails. See the Triangulation Guide. Additionally, triangulation augments traditional genealogy, so you still require a confirmed paper trail linking William to Daniel, which it seems may not exist given the comments on the profiles.
A good first step would be to find a valid triangulation to Daniel Gage, not through William. If a descendant of William then shares the same segment, that would be significant evidence in favour of the relationship, though I cannot personally say whether it would be sufficient - I would check back in at that point.