Let me first clear your understanding about curing of concrete. Curing does not mean watering of concrete what most of the Civil Engineer think it as, instead Curing means prevention of concrete from becoming dry and also any process which aids in completion of the hydration process of cement in concrete.
Like Concrete Curing can be done by ponding with or spraying potable water which normally are adopted specially in India, but curing can also be done my hot steam, by electrical methods and others.
Now lets talk about curing period of concrete, according to I.S.: 456–2000, minimum curing period of RCC Structures stands as below
a) For cases where OPC (Ordinary Portland Cement) has been used minimum Curing Period is 7 Days, but if the concrete work is done at hot and dry region then curing must be done for minimum of 10 Days.
b) For cases where PPC (Portland Pozzolona Cement), PSC ( Portland Slag Cement) or any other kind of mineral admixture blended cement has been used minimum Curing Period is 10 Days, but if the concrete work is done at hot and dry region then curing must be done for minimum of 14 Days.
It is to be noted that concrete made with OPC, PPC and PSC generally attains 70% to 85% of its Characteristics Compressive Strength in first 7 Days Only.
Now lets consider the external supporting or propping period of a RCC Structure, according to I.S.: 456–2000 they stands as mentioned below
a) For Vertical Members such as columns, walls etc. minimum propping period is 16 hours to 24 hours.
b) For Slabs spanning upto 4.5m, minimum propping period is 7 Days.
c) For Slabs spanning above 4.5m, minimum propping period is 14 Days.
d) For Beams spanning upto 6m, minimum propping period is 14 Days.
e) For Beams spanning above 6m, minimum propping period is 21 Days.
Now my point is based on the above mentioned minimum fact you have to modify the conditions in such a way that optimum solution is selected for a specific situation. Nothing can be generalized whether it can be done or not. Keep one thing in mind everything cannot be best at the same time, let us consider, say you are given 100gms of mutton, now you want to use it in roll or curry or something else you have to decide according to the necessity, if you use it in one thing then other will definitely get deprived.
Like in this case of question if you want to achieve earlier strength then you have to sacrifice the ultimate strength to some proportion, but you have to judge and select the optimum among the given set of constraints . Nothing is Impossible in Civil Engineering, we make the Civilization and others just follows on the pathway.
Note that our target is to complete the hydration process of cement, the earlier it complete the earlier everything is over, at least say 70% Hydration should be completed before turning off the curing. Also remember that even though curing period may be curtailed but the external support to the structure as props or otherwise must be kept until the structure under consideration attains the minimum strength to withstand loads which are probable to come.
Now coming to the exact point, Yes Curing period can be reduced, ways are mostly as follows
a) Use of High Strength Cement, High Alumina Cement etc, which attains required strength much faster.
b) Use of Admixtures which accelerates the whole hydration process.
c) Moisture curing at elevated temperature, Steam curing may also be adopted.
d) Keeping the whole structure warm, say a bit hot to cause rapid hydration,but it is risky and costly.
e) If your sole purpose is to avoid water ponding or spraying specially on roof, then Membrane Curing Compound may be adopted.