Is this sentence grammatically correct?

It seems quite correct to me; I see no mistakes.

Edit: That would be correct as well.

Unfortunately, neither sentence is absolutely correct. This is how sentence 1 should be written:

1. If you study Robin Hood and David, you will notice immediately that they are both especially loyal: Robin Hood to his Merry Men; and David to his people.

Your version of sentence 1 begins with an unrelated participle. "During a study of these two men", if it is read in isolation from the rest of the sentence, tells the reader nothing. The reader must read to the first comma before he gets an idea of what the sentence might be about. However, "If you study Robin Hood..." puts the reader in the picture straight away. "Merry Men" should have capital letters, because we are talking about a particular group of people, not just men who happen to be cheerful.

Now, sentence 2 should be written like this:

2. Robin Hood is willing to give his life, at any time, for his Merry Men.

"Robin Hood is, at any time,..." 'Yes,' says the reader when he gets to this point, 'but Robin Hood is exactly what at any time'? So, the "...at any time..." should follow the "...give his life...", because Robin is ready to die, whenever he is required to do so, for his men.

And, finally, (just a small point); I rather think that you should have written "If not...", instead of "If so." I wish you well.

yes