You can, but it's definitely an uphill battle, especially at D3. There are a lot of factors to consider before you decide to take on a D1 sim. For instance, were you on the recruit first? If so, how long before the D1 team showed up? Do the recruits preferences match up with your team? Does the recruit want to play? If yes, can you off a start (and minutes) while the D1 team can't?
According to Seble, the Sim team will continue to recruit "as long as it thinks it can win," whatever that means. So once the Sim offers a scholarship, you're done. If that doesn't happen, you have a chance.
It's also important to note here: Since you are a D3 team going after a D1 recruit, he won't sign with you until the last 24 hours of the second session. While he can sign with the D1 Sim at any time, depending on the recruit's signing preference.
tl;dr Yes, but only if you're lucky.