You will definitely snare some people who don't know their lines that way, but much easier for Black is just 4...Nc6, then your e-pawn actually is hanging and there's nothing better than 5. d3, which transposes into a line more usually reached via 1. e4 c5 2. Nf3 d6 3. Bc4 Nf6 4. d3 Nc6 5. c3. I don't know if that line actually has a name. I call it the Delayed Bowdler. It's fine for White but just an equal quiet line.
4...Nc6 just falls into white's main idea (which is not robbing a piece from a noob opponent).
5.d4! is the right reaction, when it is extremely dangerous for Black to grab the pawn (actually in the main line Black can grab three pawns).
You will definitely snare some people who don't know their lines that way, but much easier for Black is just 4...Nc6, then your e-pawn actually is hanging and there's nothing better than 5. d3, which transposes into a line more usually reached via 1. e4 c5 2. Nf3 d6 3. Bc4 Nf6 4. d3 Nc6 5. c3. I don't know if that line actually has a name. I call it the Delayed Bowdler. It's fine for White but just an equal quiet line.