Tim made some excellent points! But to add a few more thoughts.
One thing that jumps out at me when you go from super light to much heavier strings is that the nut slots may need to be examined to be sure the strings are not too tight in the slots. You want to be sure the strings actually fit into and bottom out in the nut slots.
Ideally you don't want too much slack in the nut slots which could contribute to buzzing and other issues. But I once went with heavy bottoms on my Taylor 814 that had a new nut set up for lighter strings and at least one of the strings was so tight it had no sustain (almost muted) because the nut was restricting the vibration of the string. A qualified guitar tech or luthier can file the nut slots to make them larger if needed - but again you don't want them to wide or too deep.
The other point is that heavier strings would require higher tension to tune to standard pitch which would normally indicate a tightening of the truss rod to compensate (although Tim's point about individual preference on action height should be noted). But if you plan to use a drop tuning, the strings would require less tension to tune than they would to standard tuning.
So depending on your preferences in general and the tension on the new strings with the drop tuning you choose, you will want to check the entire set up to be sure it is optimal for you personally. This would potentially include looking at the nut slots, nut height, saddle height and truss rod adjustment. After you get those pieces where you want you will almost certainly need to adjust the intonation which would likely change with the alternate tuning regardless of string gauge.
It is not likely that with the change in string gauge and the change in tuning, that the guitar will be set up just perfect according to your preferences without at least some minor adjustments.