TLDR: Absolutely not unless the person qualifies for an established "support of the needy" program... and it wouldn't help anyway, and they should just give money to the widow directly.
Nonprofit expert here.
As a rule, no...
This is what the IRS calls "private benefit" (or "inurement" if the private party is influential). The nonprofit 501(C)(3) tax system has a long legacy of abuse, and private benefit is the most common fraud. Everybody wants to transfer money to another person without first paying income tax on it!
This is made more perilous for churches because they automatically are entitled to 501(C)(3) charitable tax status. That means the founders aren't told of this in advance, by filing the enormous Form 1023 to apply for tax status and its numerous admonishments; nor do they seek professional help filling out the form, who would set their expectations correctly.
But even for churches, it's so important that IRS dedicates a whole page to it in their guide for churches (Pub. 1828); it's the first major topic they cover.
That said...
Aiding the destitute is a recognized charitable purpose
And churches are allowed to have support programs for the needy. But IRS requires that this be a program established as a matter of policy, and applied even-handedly to those in the community in need.
IRS is very much on the watch for cases where a 501(C)(3) organization "develops a program" for helping the needy, applies it to one single well-connected member, and then never develops the program broadly. Because this abuse is so common, the penalties hit like a freight train, including very punitive excise taxes and revocation of the 501(C)(3) tax status.
It isn't worth it anyway
The average giver can't take charitable deductions anymore due to tax code changes (that "tax form on a postcard" that president #45 created.)
A taxpayer can take the standard deduction, OR, they can fill out 1040 Schedule A and itemize their deductions. Schedule A is where you claim a tax deduction for charitable contributions. If they don't file Schedule A, they don't get any tax benefit for charitable contributions (or a very de-minimis benefit, e.g. $100).
The "Tax form on a postcard" changes, the 2017 Tax Cuts and Jobs Act, perhaps to eliminate two lines, removed the "personal exemption" (then around $5000) and folded it into the "standard deduction" (then around $5500, raised to $12,000). This meant a huge swath of the middle class no longer had to file the Schedule A (good), but also no longer got any tax benefits from charitable giving (very bad for nonprofits).
Unless you're in San Francisco or Manhattan, most likely most of your parishioners wouldn't enjoy any tax benefit anyway by piping the money through the church. They might as well just give it to the widow directly.