OTL the British Imperial forces had the 'Black Cats' the 17th Indian Infantry Division which was not then the Elite jungle fighting formation it became but a very green under equipped unit and the Burma Division which was a militia unit in all but name.
Added to this just before the fall of Rangoon was the 7th Armoured Brigade with 2 Veteran Tank Battalions of Stuart Light tanks.
9 Chinese Divisions (including 3 descended from German trained units) were also in Burma but further North and West protecting the Burma Road.
A Chinese Division was deemed (rightly or wrongly) as the equivalent in fighting ability as a Western Brigade (again not all Divisions and Brigades are created equally) and some of them fought very well during this part of the campaign.
Following the duel defeats of Bilin River and then the disaster at Sittang Bridge (that left 2 of the 17th Divisions 3 Brigades cut off) the unit was shattered as a fighting force and lost much of its heavy equipment and had suffered heavy losses in personnel (with many of the personnel having lost their personnel gear getting back across the river)
Against this the Japanese had sent 2 Divisions the understrength 55th and 33rd (each minus a rgt/brigade) from Thailand and a platoon of tanks to capture Moulmien and then advance to the Sittang Bridge (fighting the Battle of Bilin River) and then to Rangoon.
The logistical situation was that it was virtually impossible for the Japanese to maintain much more than this force from the Thai border and only additional forces were sent once Rangoon was captured adding 2 more more Infantry Divisions and 2 Tank Regiments.
So the capture of Rangoon is vital to the Japanese war aims in Burma - the campaign cannot be conducted with overland supply lines from Thailand
So enter the 6th and 7th AIDs eh?
A political hot potato but ok
Both units by Western Standards were very powerful infantry formations each with more artillery than the entire Japanese force (each division would have 72 x 25 pounder in 3 Regiments) and unlike the 17th Indian and 1st Burma Divisions had quality equipment and well trained officers and NCOs.
So had they arrived before the Japanese invaded then their impact would have been massive and the 33rd and 55th IJA divisions would not have been enough IMO to kick the 'British' out of Eastern Burma and Rangoon.
Could the Allies have maintained a position at Rangoon with any convoy to the port now being under Japanese air range - I am not sure but tehy would have far greater options to have done so and waited for the weather to end any effective campaigning from the end of April (till Nov)