This is highly variable. Each university has its own set of rules and regulations involving promotion and tenure. There can be a range of requirements related to teaching evaluations, research output, service requirements, and community outreach in addition to external funding.
For example, at my institution it is standard to apply for tenure in the 6th year. It is possible to apply early (though I think this means in the fifth year, and not at any time; I would have to read the fine print). Hypothetically, a big grant would look very nice if I were applying for early tenure. But I still have to meet requirements in all of the other areas. No matter how big the grant was, I would still need to meet the requirements in the other areas to be granted tenure.
Also, if Bob was bringing in less grant money than I was, it is likely that there is not much that he would need to compensate for. If he is applying to grants and bringing in SOME grant money, and meeting the requirements in the other areas, we are both likely to be promoted on the same schedule. Although yes, in the case of early tenure, Bob might have better luck if he has stellar teaching reviews, this will show he is exceeding expectations in at least some areas to justify being granted tenure early.
This is of course specific to my institution, which is a public institution focused primarily on teaching. There are quite possibly institutions where external funding is the #1 thing they look at when dealing with promotion.