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We know that 1. e4 e5 2. Nf3 f6 is a disaster for Black (Damiano Opening).
But White has an extra move. Can he therefore play 1. e4 e5 2. f3 ?
If Black replies 2... Nf6, White has 3. Ne2 (followed eventually by Ng3). That seems to stave off the immediate problem of the Damiano Opening.
So does the extra move give White enough leeway to play like this?
The only thing 2. f3 can possibly achieve (for its many obvious downsides, as pointed above) is that it supports e4 right away. If that's the reason why you would consider playing it, then play 2.Nc3 instead. Even 2.d3 is playable and can transpose into many Ruy Lopez systems or the English opening. Here's a somewhat related post, where an early f3 is playable, as it allows white to get a stronghold on the center: Early f3 in d4 openings?
2.f3 looks like a terrible move. It wastes a tempo by not developing a piece; it takes f3 square away from the knight, and it weakens a7-g1 diagonal, while achieving absolutely nothing. I think that after any normal move (2...d5, 2...Nc6, 2...Nf6, 2...Bc5) black has the edge.
While I don't see any reason to give up the advantage so early, I don't think white is lost (just slightly worse), so white can play it if they want to.
I also think that 1. e4 e5 2. Nf3 f6 leads to a "disaster" is an overstatement. 1. e4 e5 2. Nf3 f6 3.Nxe5 fxe5?? does lead to a disaster; however, black can play 3...Qe7.
2..f6 was a horrible move, but it was named after him :)
That's ECO C20, the King's Head opening. It does not appear in my masters' database. It appears at the amateur level with Black winning about 80% of the time.
I would say no, it is not a preferred opening.
Why would you want to even play f3? You're white, you don't need to defend at the beginning of the game and E4 doesn't need any help at this point as nothing is attacking it.
The only time I can see f3 being viable so early is if you allow black to take the pawn on e4 thereby offering a sacrifice of a pawn in exchange for development of the knight. However this is more common on d4 and c3.
