Is it possible to use a freelance fundraising consultant and pay them on a commission basis only?

It is possible to recruit somebody and pay them on results, but this is highly unusual, and it is unlikely that a professional, experienced person would accept these terms. Writing grant applications takes time and effort starting with the research required to understand the project and source potential funders, checking their requirements and eligibility, looking at the types of projects they fund and then developing and writing a proposal. 

Even high quality proposals have no guarantee of success because of the sheer competition for grants, as well as other factors beyond your control such as a possible long-standing relationship with a funder, a personal connection, or even personal preferences of the assessor with regard to the type of project submitted. 

These have no bearing on the quality of the proposal and it would not be ethical to request funding for a project and use some of the grants to pay commission for a consultant unless you can clearly demonstrate this in the budget you submit as part of the proposal.