Yes, generally.
However, the 501(c)(3) may have some vulnerability, and so could you, depending on the exact facts.
In general, the donor should be donating to the organization, and the organization should have a defined decision-making process (like a board of directors or executive committee) to decide how the money will be spent. If the donor exerts too much control, the donation may not be tax deductible. For example, if a church asks for a special collection to buy a new piano, and you donate to that special collection, it's just as deductible as your regular tithing. However, if you go to the church and say, "I will donate $5000 but only if you use it to buy a piano" that runs a risk of being too self-directed. And if you say "I will donate $5000 but only if you use it to buy a piano from the piano store where my girlfriend works" that's not deductible to you and it is likely a violation of the church's non-profit status to agree (self-dealing).
If there is more than one person working at the charity, it would also be good for someone other than your relative to process the donation and issue a receipt, so there is a someone double-checking the transaction who is not related to you.
Basically, you want to keep the relationship professional and as arms-length as you can, given the circumstances, so that if there were any questions, it would not look like the charity was abusing its status to your benefit.
