Can one compensate for poor funding performance elsewhere in determining academic promotion? Follow up question to How does research funding work in determining academic promotions? since it was too broad.

Take two equally talented researchers, Alice &amp; Bob. To what extent will it matter if Alice has a large amount of grant funding, compared Bob who has little or no grant funding? Can Bob compensate for his lack of grant funding by, e.g., having better teaching evaluations or supervising more undergraduate students?
Like your other recent questions, this depends on many things, but most especially on the mission of a given institution. In some places good research would vastly outweigh good funding. In others, just the opposite. In teaching institutions, as opposed to primarily research universities, teach might outweigh everything else by a large margin. 

But there are certainly institutions where the only viable path to tenure goes through the funding institutions and a successful and continuing record of attracting money. I some of these, the research is actually primarily carried out by the students, not the PI, though under the direction of the PI who is able to fund the lab and its student researchers. 

So, first look to the stated mission of the place before making any assumptions. Then make sure that the actual mission is consistent with the stated mission. Sometimes they are at odds for various reasons.