So Metal Bat is capable of doing a swing which destroys a building. For doing such a swing he would need an incredible strenght and for having that strenght he would need a very hard body (arms and fits included). What does the bat add here? Does Metal Bat need his bat for being more powerful? Has he ever been shown fighting without the bat and being very powerful too?
He indeed has an incredible amount of strength. From the One-Punch Man Encyclopedia,
When the intensity of Metal Bat's anger reaches its maximum, his power approaches infinity.
Aside from that, he also has extreme durability, enabling him to take many hits from higher-level monsters.
From one of the omake, it was said that he only acquired his unbreakable bat upon his promotion to S-rank. This means that he does not need the unbreakable bat that was made for him in order to defeat monsters, as any other bat would do, albeit it would break easily, as shown in the same omake.