Alan Keyes was/is a birther. His support among the conservative base is probably roughly equivalent to that of Steele...meaning not much. If Steele would have pushed birtherism, he would have been run out of the party before the end of his chairmanship term.
And Steele was already having fundraising problems. As a vote of “no-confidence” of his leadership, donors were bypassing the RNC and sending money directly to candidates, or to the Rove and/or Dick Morris fundraising groups.
Just my opinion, but I believe had Steele, as the head of the RNC, decided to embrace birtherism, he would have been forced to resign in less than 24 hours.