Not really. Let me paraphrase a bit.
To determine if a link was sent, more context would be needed.
We have an event, and we don't know the result. But we want to do something to find the result. If we assume it was sent, and test accordingly, we are dealing with a hypothetical situation, also call irrealis mood. Would is used in this context when we have no firm expectations or wish to convey an unbiased attitude.
There are some exceptions. If you want to convey an expectation that the assumption will turn out to be true, you can use the indicative mood. Making that point clear will normally benefit from some minor rewording.
To determine that a link was [actually] sent, more context will be needed.
Using may here changes the focus of the statement as well as the meaning. It asks a question about the context, instead of concentrating on the question of whether the link was sent. Presumably, you want a reliable way to determine whether any link gets sent, not just do so in this one instance, so may doesn't work here.
One other point. This modal would is used as a polite way to make requests.
Would you mind if I borrowed your car for an hour?
If the statement is a polite covert request for more context, then there is more pressure to choose would.