Viable yes. Power fist for HtH and Super Sledge for melee. HtH also gets the Slayer perk which a d10 is rolled and if the number is equal to or below your Luck stat, you'll get a critical hit. This is a level 24 perk, very late game, but if you have a high luck stat, most of your hits will be critical.
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Any kind of build is viable in Fallout. I did beat it once with a full melee character, and the game ended up being easier than I thought. Not only you can be VERY strong and hit enemies' weakness easily, but you also don't have to worry about ammo or anything. ;)
No enemy ever did gave me a headache, I just had to be carefull not to start fights in the middle of a city with a fully armed population. :p
BTW, the mutants that have bazookas are fun! :p They sometimes shot missiles up close (stupid fellas!), giving me quite a good wooping, but they DO get hurt in the process too. Most of them, though, just try to get away from you before shooting, and end up without enough AP to shot after moving. :p
:3 Everything is nice and cool... until the roach starts to fly!