Is it reasonable to assume that the battle of Stamford bridge weakened the Godwinson forces enough to ensure their defeat at Hastings?

Taking this question literally, the answer must be "no". Hastings was a close-fought battle, and it could have gone either way. Despite his losses at Stamford Bridge, Harold Godwinson had a reasonable chance of victory at Hastings.

Three things made Harold's chances significantly worse. First, Harold expected William's invasion to be earlier, and had assembled his fleet and an army; the bulk of his army from probably from the fyrd (militia). When William didn't arrive, and the term of service for the fyrd was over, he sent the men home, and also the fleet. This had two important consequences: the fleet wasn't available to stop William's invasion at sea, and fewer men were available to fight William when he arrived.

Second, Harold's army did take losses at Stamford Bridge, and was weakened by this. We don't know by how much.

Third, Harold and his army were in the north when William invaded. This slowed his response. In principle, Harold could have waited for more forces to join him before fighting William at Hastings, but he fought with what he had (perhaps because he thought his army strong enough, and perhaps because he felt he couldn't wait any longer).

The first of these was independent of Harald Hardrada, the the other two are consequences of Harald's invasion. If the English army had been able to beat Harald at Fulford, things would have been different: Harold would not have needed to go north with his army, and if Harald Hardrada (and Tostig Godwinson) had been decisively defeated at Fulford, some of the northern English army could have reinforced Harold.

Harold spent a week in London after returning from the north, before going to fight William. This time might have been used to collect more forces, to make up for his losses at Stamford Bridge. It is quite possible that if he had been able to stay in the south, the main difference would have been an earlier battle at Hastings, with similar forces involved.

In summary, Harald Hardrada's invasion certainly didn't help the English chance of victory of Hastings, but it might not have hurt it much. Or it might have hurt it a lot!