I see. I had forgotten the OTL 1844 election was so close; for some reason I was misremembering it as the Whigs decisively being thrown out after the disaster of Tyler. If it was that close what with everything in OTL, then this does seem plausible.
Which could raise a question about an 1842 election. Pretty clearly, that will go ahead only if the Whigs are 100% certain of winning it. If they have the slightest doubt about it's outcome, expect a hasty Act of Congress (no problem there as both Houses are Whig in 1842) rescinding that provision and leaving the PPT in charge until 1845.
This could cause real fun. Until 1890, the PPT was normally chosen only for a particular session. OTL, this didn't cause any turnover, as Mangum was left in the chair till 1845; but TTL the position carries with it the Acting Presidency of the US, and so is a far more valuable prize. Expect some fierce infighting among Whig Senators.
Throw in a death or two by accident or illness (19C Washington was a notoriously unhealthy town) and you could easily get half a dozen Presidents in four years.
As a matter of interest, does anyone know what salary Mangum would receive? Would it be just his normal one as Senator, or would he get the salary of a POTUS while exercising the powers and duties of that office?