Given that Grant won the popular vote in 31 of the 37 states in the Union, a realistic scenario for a Greeley victory is difficult to imagine. He would have had to win the popular vote in the 10 states where Grant's margin of victory was under 8% in addition to the 6 states he won in OTL (his MoV was below 8% in 3 of those states) in order to secure an EC majority (177 were needed to win and w/those 10 states added to his OTL total gives him 179 votes); not an easy task to be sure.
However, had he managed this upset victory and received the majority of EC votes and then, before the votes were counted by Congress, died, Congress would have no option other then to declare Greeley & Brown the winners - Greeley having been alive at the time of the EC, thus making his votes valid - thus making Brown the President-elect, in accordance w/the Constitution.
Now if the victorious Greeley dies as per OTL, then his votes would be scattered among various prominent Democrats (as they were in OTL), which would most likely leave Grant w/a plurality of the EC votes. The presidential election would then be decided by the House, with each state delegation having 1 vote. At the time of the vote, February 12, 1873, 21 delegations were GOP majority, 14 were Democratic majority, one was evenly split with 3 R & 3 D and one was split with 4 D, 3 R and 2 Lib. R. In an election between Grant and the two top recipients of Greeley's votes, Grant wins easily. Additionally, Benjamin Brown becomes Vice President come March 4, as his EC victory would not be affected in this scenario.