Temperance has already estimated things pretty nicely.
But nevertheless - how would you handle the Raid clears, especially current content (MoP)? You still have a significant amount of trash between the bosses. You cant have a raid clear only the trash and not the boss.
Either you have to have a raid - that you are a party of - who clears ToT with you. Or you need to be ported out / in between the bosses. Like for instance you could be ported in for Jinrok after the first trash has been cleared - then port out to a 5man heroic after jinrok is down - then get ported back in (or to the entrance at least) for horridon - out again after to clear another heroic and so on. That means you have about 10 minutes for a heroic clear between trash pulls without losing too much time I guess. But even that adds alot of movement time inside the instance. You need to walk from entrance to horridon, from horridon to council and so on. Thats another minute each boss that hasnt been accounted for yet. And - you need to clear 10 man heroic Raden (as mentioned above, you need to kill every optional boss like sinestra so that should also include raden!?). Not sure you're able to down every boss on the first attempt. Sure, Jinrok should be no problem. But somewhere someone always fucks up. And if you're fighting Animus / Lei-Shen / Ra-Den its more than possible that you whipe 1-2 times on those bosses. Even if you walk up to them in 550 Itemlevel.
Maybe you could use 2 ToT Ids? Clear everything on NHC up to Lei-Shen then take an existing 11/13 HC cleared ID and only to lei-shen and raden heroic? Of even only Raden? Not sure how all that lockout stuff works, but might be possible. If thats possible you could shave off alot of minutes off the boss kill length estimated by Temperance. Then you will only need like 3-4 Minutes in average / boss if you do them all on nhc.
I would remove SoO from the list Temperance provded as it is not listed by the OP. The estimated 104 for ToT could be cut at least in half then if you can do it as mentioned above. 96 + 52 Minutes = 148 Minutes or 2.5 Hours shaved off.
Meaning you would only need 23.5 Hours (again taking the values Temperance provided).
So I guess it could be possible if all stars align and you have like 20-30 People helping you, including 4-5 Warlocks and a 550 Itemlevel geared ToT Heroic Raid.
If you don't do it solo but as a 10-man team however, I guess you could very well do it. You would shave off significant time off of all the other Raids. Especially those 5 minutes for all the cata bosses. And the 8 minutes of the earlier MoP bosses.
If you have the gear, those MoP bosses - especially on nhc since there arent any bonus bosses - will fly in a matter of minutes. 2-3 minutes tops for each boss.
You just need to make sure that 1 player is always there for every kill.
You could also have 3 people of that 10-man raiding team aim for the world record. Meaning those 3 will do every heroic together etc. It wouldn't really net you faster heroic clears, as you are limited by the instance limits anyway - but it would reduce the chance of failure. 24 hours is a long time and if someone would need to drop out for whatever reason, you still have 2 fallbacks.
So I guess if the rules where changed abit or clarified in how exactly you need to do this in order to qualify, then I guess its totally possible.
As someone said already, it might also be possible to get in a full CM Gold clear (instead of doing the MoP heroics on heroic mode) if the parameters fit. If you really have a 10-man heroic team assisting you it should be no problem to fit it in. As you are limited by the 5? instances / hour anyway you wouldn't even lose too much time doing the CM Gold clears (even if you play them safe and dont go for world best times).