I have had this conversation over and over in the offseason.
It is possible for a team to win without much power. But the odds aren't good. I don't think it is "Dumb and Dumber" so there's a chance odds, but not good. Right now the above average team HR teams in baseball are:
1. Houston (148)
2. Milwaukee (138)
3. Texas (135)
4. TBR (133)
5. NYY (132)
6. NYM (129)
7. LAD (127)
8. Cin (125)
8. Oak (125)
8. Was (125)
9. Balt (123)
10. CHC (117)
11. Tor (117)
12. Arz (113)
League average is 111.
The Braves have 88, one ahead of Pittsburgh and 13 ahead of the Giants for worst in baseball.
In the bottom half of baseball, KC and STL are the closest to league average with 107. Colorado has 104. Cleveland has 103. Seattle 101. Minnesota 100.
Boston is the real anomaly with 92 just 4 more than the Braves. However, they have the 4th best team ERA in baseball behind the Dodgers, Cleveland and Arizona. (The Braves have the 7th worst team ERA in baseball).
This is one of the areas where I think the whole idea of WAR breaks down. If you have a team where every player is a 3 WAR guy theoretically where one teams players don't hit for a lot of power, have excellent defense and base running where that makes up a significant part of their value, playing against a team of 3 WAR guys who hit a lot of HR, play decent defense and don't steal bases, then the power team will win most of the time because when you hit a single and steal a base there's still a good chance you won't score. Whereas, when you hit a HR you score at least one every time.
But, power is weighted more heavily in WAR so I'm confused by your logic. If a non power guy is a 3 WAR player, he's hitting a **** load of singles then.