As a regular 3, ... Be7 player, I can say that Be7 is not played to give an immediate check on h5h4. As others pointed out the best move is 4, Bc4 but white must be aware of the several tactics that could arise in this position. For example after the natural 4. Bc4 attacking the f7 pawn,
[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Be7
4. Bc4
Black would simply develop his knight to f6.
[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Be7
4. Bc4 Nf6
The idea is to attack the central e4 pawn and plan a trick if white tries to protect the pawn by 5, Nc3 then comes
[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Be7
4. Bc4 Nf6
5. Nc3 Nxe4
if 6, Nxe4 then 6, ... d5 wins the piece back with a fine position.
[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Be7
4. Bc4 Nf6
5. Nc3 Nxe4
6. Nxe4 d5
I have seen most players would give back the piece immediately after 5 ... Nxe4 by 6, Bxf7+ Kxf7 and then 7, Nxe4
[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Be7
4. Bc4 Nf6
5. Nc3 Nxe4
6. Bxf7+ Kxf7
7. Nxe4 d5
This is a perfectly playable position for black. The king could seek shelter in g8 after developing the rook to f8 or e8. The bishop at e7 guards the possible knight maneuvers and there is no real threat of decisive attack in this position.
There are many more interesting variations after 4, Bc4 but I am stopping here as the OP would likely be able to discover them without much effort.