Yes and no.

It's an attempt to understand the biblical text literally and then shoehorn events and people into that text. There are a (few) people left who will argue for an early Exodus, and they tend to be of the fundamentalist sort (see Petrovich's neverending article for an example of this - he and Bryant Wood (his mentor) seem to be the only ones at this level). Most other people will argue for a later Exodus (13th century) or perhaps exodii which is later aggregated into one story. The majority of those who will argue for a historic exodus (as in, it happened, but not in the way described) will plonk for a 13th century one. So there is a continuum of argument about when the Exodus happens - if you want literal, it's the 15th century, if you want the best scenario, it's the 13th.

The problem is that if you want to do this, you have to line up all the other ducks in the story such as the destruction of the Canaanite cities and these dates don't all fit together with either a late or an early exodus (some do, but others don't - the dates are spread over time).

Thutmoses III launched 17 military campaigns until 1446 BCE at which point they ceased

It's pretty certain he did 16 campaigns. There's a reference in col. 107 which might indicated Thutmoses was in Asia, and if so, it could be 17. The battle annals which describe all his campaigns stops at year 42 but TIII lived for another 12 years. It's probably that things still continued afterwards, but they simply stopped recording them for a number of reasons other than his army being drowned. The Medamud text mentions Thutmoses campaigning in Syria after year 42 and there is the possibility of coregency campaigning with Amenhopsis II.

The dates for his reign are fluid because of the uncertainty of when he started reigning. It's normally around 1479-81 BCE, so the 1446 is roughly in the ball park, but as the website(s) no sources, I'd like to know how they got that number. I've seen quite a range of dates for Thutmose so it could just be who you choose to follow for your dating.

Also in the section '16 reasons why Thutmoses III is the Exodus Pharaoh, reason 16 saying that the Amarna Letters mention 'Habiru' conquering Canaan?

It's funny that they'll use Kitchen for the support of the Apiru but completely ignore him when he says it's a 13th century Exodus and conquest. I wonder how they rectify him with 'bible trashing archaeologists'. Kitchen isn't equating the Hebrews with the Apiru and he says that at the beginning, the very part they begin the quote with so I'm uncertain how they get this. He's simply saying that the behaviour of the marauding bands was analogous to the Hebrews. Problematically, the Habiru status and identity changes depending on who is talking about them - Wiki has a long run down on this. There is no connection linguistically between Apiru and Ibiru.

As I said earlier, without citing any sources, it's impossible to see how they get the connections they do. The sources they do cite don't necessarily say what they want it to. This is a great example of "I have a theory, what bits can I fit into it". Sometimes it works, but this isn't one of them.