I think perhaps we are all going a little more deeply into the OP's question than is really necessary.
If I understand correctly, OP has a paper trail to a person called Philip Small who would be their 2X great grandfather. OP also has a possible candidate, and has made contact with a person directly descended from this possible candidate.
Assuming both of them are correct, that would, I think make them 3rd half cousins (if the person contacted is of the same generation as OP - a remove or two if they are not).
I may be mistaken, but I think the chances of that close a match not registering as a DNA match are very slim.
So assuming all the above to be correct, I think the simple answer to the OP's original question is YES, if you are correct, a DNA test taken by you both should produce a match.