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This question comes up quite often amongst amphibious aficionados. The correct answer is that we won't ever know, naturally. The other correct answer is no, they wouldn't have made much difference. The LVT's natural home is in the intertidal area.... https://twitter.com/NickHewitt4/status/1355465937781190657
The troop carrying LVT is far less efficient at sea than landing craft, which can carry more men, faster. Once onshore, what then? Does the LVT go back to sea or hang around? If the former, why use it over landing craft? If the latter, there's a bigger consideration...
LVTs in your task force have to displace other equipment – less tanks & trucks for the infantry and less landing craft for the navy. Minor landing craft were bigger and faster than LVTs and could shuttle back and forth – the Allies had few enough for this ferry service as it was.
LVTs replaced landing craft in the Pacific where the geography made the landing craft unsuitable (offshore reefs etc...). This wasn't a problem in Normandy, so there was no need to replace a perfectly suitable vessel with a much less efficient one.
There's a bit more of an argument for the armed and armoured LVT (A) being used, but even here I disagree. In theory they could have replaced DD tanks, but I'm not sure they could have been much more successful, and they wouldn't have had given any greater advantage inland.
Nor would they have had any advantage operating offshore, where they would have simply displaced very efficient and effective support landing craft, and almost certainly done a poorer job.
So using either type of LVT would have been using a jack of two trades (land and sea), but a master of neither. And you'd have to displace the masters (tanks, landing craft) to accommodate the jack. It's a bit like using 2-1 shampoo – it doesn't do either job as effectively.
