Possibly, though OTL he was married for ten years with no children, which suggests that either he or his wife Anne Stafford was infertile. Anne outlived him by seven years and had two children by her second husband, the Duke of Exeter, so probably Edmund.
In which case Conisburgh, now the Duke of York, will be the "Yorkist claimant" circa 1450. He would then be 65. Or he might assert himself sooner. He would be a major player in English politics throughout the 1420s, whereas the younger Richard had to wait for his majority in 1432. If as OTL, Mortimer and Henry's two brothers die without issue (and his two sisters, who married continental princes, also have no issue as OTL), then Conisburgh's claim becomes very cogent and IMHO he would assert it. At the very least, he would insist on being recognized as Henry's heir presumptive.
Then if as OTL Henry goes mad... Conisburgh could be effectively Lord Protector, Having charge of Henry, he could insure that Henry never marries, or is kept away from his wife, even if he regains his sanity. Or the paternity of any royal children could be questioned.
Of course, now that I think about it, it's unlikely that Conisburgh lives that long; he probably dies around 1440, aged 55. That would leave young Richard in a position similar to OTL, but IMO much stronger.
