Does studying up on a particular opening help you at all with its reverse opening, i.e. the Sicilian and the e5 variation of the English?  Of course, the move order cannot be exactly the same for one reason or another, but as long as the pawn structure remains fairly similar (just reversed), then would the general plan/idea of each player be similar as well?

I asked the exact same thing a yyear ago and someone told me no but I cant rember why. its in my archive on chess.com but since I cant rember it must not have been a really good reason anyway.

I will only say that I play chess somewhat instinctively and have good luck with the dutch defense against the english opening. It stands to reason that it should considering the space and time dynamics when comparing e4 and the sicilian. I realize it is slightly different overall, but in the center, you have some of the same type of scenarios playing out.

As everything in chess the correct answer is .. it depends ..

White has a tempo more. That leads to different play. In the dragon variation of the sicialian the white attack with the h pawn is very dangerous and in most dragons it is used. With 1 tempo less the h5 is a lot less dangerous and is rarely used.

In other variations you can use idea from the sicilian but having a tempo more can either be a advantage of disadvantage you cannot presume that because you have a tempo more it must be a better version. For example in the sicialian black can often choose where the knight will be placed best. At c6 or ad d7 while in the English white practicaly always commited his knight to c3.

So in other words .. no

From my own experience, the extra tempo makes most reversed openings a completely different bird than their mirror counterparts. About the only thing you can sort of take from both is common pawn structures (like in a reversed Nimzo-Indian).

To the extent the pawn structures are the same, the same strategies apply.  But as moonnie and FirebrandX mention, the extra tempo makes a huge difference in the opening play, so the opening variations don't mirror those of the defense.

And since defenses are set up primarily to counter, the reversed line isn't guaranteed to earn an advantage even with the extra move.  In fact, most of them aren't particularly challenging to Black.