Yes, it has. Bush and his team courted the scared white people demographic and told them their way of life was in danger unless they hated Muslims, homosexuals and all people in the not-white category. He got their votes. When Obama became president, that scared white people group freaked out and formed the Tea Party, which has nearly ruined our country. And all because of Bush's election strategy.
Bush's legacy did hurt the GOP and it hurt the GOP badly. But, it has gotten worse since he left office with the congress that is now running the House of Representatives. The United States is a centrist country and the GOP have gone so far right, many are turned off to it.
Many who have carefully studied the way that the GOP has evolved over the past few decades will have to acknowledge that the party has abandoned its roots and become something much different, and at this point in time it is the presidency of George W. Bush that sticks out the sorest.
No, Bush's legacy has not hurt the GOP, because Bush was generally liked by conservatives. In Texas, he is revered, as is the entire Bush family. The GOP's problem is the GOP. They do not want to listen to the people who actually cast the votes. They are elitist and out of touch.
President bush has not hurt the Republican Party. His stature has risen in the past few years, when people compare him to the horrible job the president Obama is doing. He could even campaign for some politicians and help them out if they are from some states that are friendly to Bush.