Can a Gradient Boosting Regressor be tuned on a subset of the data and achieve the same result?
You should never train or do grid search on your entire data set, since it will lead to overfitting and reduce the accuracy of your model on new data. What you have described is actually the ideal approach: do grid search / training on a subset of your data. Yes, your model will get different results vs if you used the entire set of data, but your model will be much stronger because of it. 

For more details on why you would want to split up / sample your data, see this quesiton: https://stats.stackexchange.com/questions/19048/what-is-the-difference-between-test-set-and-validation-set