I can see a Japanese military invasion of the Bengal from Burma turn into one big clusterfuck.
It would make for a dangerous development anyway. Before the invasion can be properly launched (in fall), several thousand miles southeast Watchtower-Guadalcanal would end quicker in an American victory, in, say, a couple months, due to less Japanese land forces committed, with mostly naval losses. In New Guinea MacArthur, on the other hand, has even more of a hard time on the Kokoda Trail (where the Japanese haven't squandered their force in the suicidal march across the jungle to Port Moresby).
Then, right when the British are putting their maximum effort at El Alamein, the Japanese strike into India, after strong-arming even Thailand into providing at least a division for the effort. The operation is two-staged. Their first objective is the coastal area of Chittagong. When most british forces are pinned south, they strike north in the general direction of Dimapur.
The final target of the first phase of the campaign is gaining the Meghalaya hills and most of the Assam plain, thenhead straight into Bengal proper to Kolkata, with a flaking movement from the north which by that time could be assisted by (light) armor.
Would that succeed? Difficult to say, but probability is better than in 1944.
It is likely that the Americans would have to divert significant forces, especially aircraft and tanks, from the Solomons and New Guinea to the Indian theater at the end of 1942: it could even adversely affect the prosecution of Torch towards Tunisia, allowing Rommel precious time to regroup, recover and attack into Algeria along with the Italians.
And the prospect of massive unrest between the Indians is not so unlikely - while I'm pretty sure that most of the Indian army would not betray the British, at least not for the Japanese.