I dont think it would affect Onaga's return much. In the original timeline, even though Shujinko was invited for the first MK tournament, he was instructed by Damashi to return to the Netherealm to regain back the 'taint' he had lost during nightwolf's soul cleansing training and he remained there till the start of MKDA, where he helped Scorpion track Quan Chi.
Thus this time around he could help the Earthrealm heroes, instead of spending time in the netherealm, when Raiden seeks him out. Plus during the war against Shinnok he would regain back the taint in an alternative way. This would also be something Damashi would support as well since Shinnok needs to be defeated for Onaga to get his amulet, which is vital for his return and rise to power.