In act 1 of Importance of Being Earnest, is what happened over the sandwiches funny?

Yes, definitely!  It might not be a laugh-out-loud, rolling-on-the-floor kind of laughter, but it is humorous and allows us to continue to sketch Algernon's character.

First, Algernon tells Jack, "Please don’t touch the cucumber sandwiches.  They are ordered specially for Aunt Augusta," who he is expecting at any moment.  However, he's been eating them, as Jack tells us, throughout their whole conversation, and he eats another one now.  So, he's not willing to share them...

Yes, definitely!  It might not be a laugh-out-loud, rolling-on-the-floor kind of laughter, but it is humorous and allows us to continue to sketch Algernon's character.

First, Algernon tells Jack, "Please don’t touch the cucumber sandwiches.  They are ordered specially for Aunt Augusta," who he is expecting at any moment.  However, he's been eating them, as Jack tells us, throughout their whole conversation, and he eats another one now.  So, he's not willing to share them with Jack, even though he's eaten several himself.  Algy is pretty selfish and cares a great deal for appearances, and based on what he's said, he seems to be saving those sandwiches for his aunt; however, his actions differ from his words and betray his lack of respect for that woman.

Then, by the time Aunt Augusta has arrived, Algernon has actually eaten all of the cucumber sandwiches.  When she asks for one, he "pick[s] up [the] empty plate in horror," and says -- in mock surprise -- to his butler, "Good heavens!  Lane!  Why are there no cucumber sandwiches?  I ordered them specially."  Lane, his butler, is apparently so used to his employer acting in this dishonest manner that he covers for him smoothly, saying, "There were no cucumbers in the market this morning, sir.  I went down twice."  This is clearly a lie, too, because, of course, there were cucumbers in the market and they were used to make the cucumber sandwiches that Algernon already ate.  It's a completely ridiculous situation.  Algernon knew that his aunt preferred cucumber sandwiches, and so he very easily could have not eaten them and avoided this whole situation; however, it conveys quite a bit about his character that he is willing to put on this little show rather than simply deny himself a small pleasure.  Lying comes easily to him, and he is quite willing to do it, especially when he will take pleasure for himself in the process.