Would a claim that a company makes charitable donations sway you to buy their product?

I'd do it just to support the premise until people start doing more of their own charity spending. But what happens is often obnoxious, like the coca-cola company with annual revenues of 16 billion US dollars, spending 100's of thousands, to advertise that they will give some student a $10k scholarship. (that was a reflection that came back during a time when I was trying to sell them a multi-billion dollar idea for 10k).
I'd rather support forward thinking companies like Patagonia who runs collective on-site daycare & brings employees on mountain retreats to discuss collaborative production & creativity.

It depends on the charity and the confidence I feel about it.

Do I need this product?

No, usually large corporations only make donations out of selfish reasons, like selling more stuff. I would buy the other, the donation has already been made anyway.

I would certainly check the charity to make sure its legit.

If they cost the same amount and are identical, of course I would choose one that donated to a worthwhile charity. However, I think that in practice, it is very unusual for products of different brands to be identical in both price and quality. Most companies try very hard to distinguish their products from their competition as much as possible in order to encourage brand recognition and loyalty.

I use Working Assets for long distance. They go to some length to have the same prices as the other major US long distance companies, and donate money to charity. The cynical explanation of their business plan is not so much that they attract customers by being socially responsible but that they get lower "churn" and thus make more money than if they didn't donate to charity. Whatever. It works for me.

If it was a charity I have heard of. Not something like the Human Fund from Signfeld.