Blood Bowl: Would a Dwarf team of mostly blockers be feasible?
No, it's not a competitive build.

Longbeards are very slow. Only treemen and mummies are slower in the modern game. Their agility is also poor, requiring a 4+ to pick up, catch or dodge, even without any negative modifiers.

Frenzy is not a weakness on the Trollslayers - it's a strength. Dwarf cages can be relatively easy to stall as it's very difficult for them to break the pattern of pillars that are often used to slow a cage down, particularly near a sideline. With frenzy you threaten teams that pillar near a sideline, as to do so risks their players to being pushed into the crowd.

Taking only one player with enough agility to handle the ball reliably is also a risk. A thrown rock or a fortunate armour roll against av8 and you will be left without the ability to score, or move more than 4 spaces without GFIs. For this reason it's more typical to run with both blitzers and two runners (though not universal).

You likely won't need five rerolls as you get more used to risk management. And you should seek out a newer version of the rules, as the one you're using is out of date - try googling LRB6, CRP (Competition Rules Pack) or Icepelt.