The United Way will allow a donor to specify a recipient. In this case, it appears that the member would like to designate the Church. After the UW gives money to the specified donors, it gives the rest of the unspecified donations to the other agencies based on a schedule of its own design. (A common misconception is that giving a specified donation keeps other agencies from receiving funds, but this is not true. The unspecified agencies just get more of the unspecified funds to make up for it.)
So the donation, in and of itself, is legit.
As for the practical matter, my company knows what a normal donation is, and they would not match more than about one of my tithing payments if I were to try and do this.
And as for another practical matter, the United Way intends to benefit local agencies. Paying tithing through the United Way, whether the member gives the local bishop's address (which could change) or the Salt Lake Address, either way tithing money does not stay local. (Yes, I know, technically some comes back through budget allocation.)
A number of years ago, our local United Way stopped allowing designation of contributions. There were too many of these types of contributions to make it worth the effort.
But to answer the question, Church headquarters can provide the number and the address. That way they will also provide the receipts and accounting and the local bishop will not have to deal with all of that after the contribution is made.