Are Good Deeds of Any Benefit to One Who Worships Others Besides Allah?

No, good deeds are of no benefit to those who worship others besides Allah.

Evidence from the Noble Qur'an
{But if they had joined in worship others with Allaah, all that they used to do would have been of no benefit to them}, {Soorah al-An'aam, verse 88]

Evidence from the authentic Sunnah
((Who ever does any deed in which he associates partners with Me, I reject him and his Shirk)), [Transmitted by Muslim]