Well, that's a subjective question; was it crucial? We have no idea what England would have looked like if the Normans hadn't invaded; would the Godwinsons' descendants rule for 1000 years like William's? Would England had conquered Wales and Ireland? We don't know.

But some key things I'd say are: French land provided the Kings of England with valuable money (when Mary lost Calais, it was the most profitable city in England for the Crown), possibly contributing to their strong position compared to many other monarchs; The replacement of Anglo-Saxon noblemen with Norman barons also fortified the position of the King, and led to a more unitary state; Due to arguments about the position of the Duke of Normandy/King of England in France, France and England were engaged in a long series of wars, thus creating an enduring enmity that only faded in the 20th century with the entente cordial; Norman culture was strongly supportive of foreign invasions (see Sicily). Harold Godwinson probably wouldn't have invaded and conquered Ireland. So, one could argue that without the invasion, England would have been a less centralised state (like France or the HRE) and would not have conquered Ireland (at least, not so early).

But I feel that this question is in some ways speculative. Could you perhaps pose it in a different way?