I've never heard of an employer pursuing an employee in this way. Theoretically, they might be able to take some legal action, but why would they bother - it would cost them a huge amount of time, effort and money.
Are you sure that your current employer will still see you as a key team member. As a manager, I feel that once someone hands in their notice, it is often better to let them fly. Their commitment to the organisation is usually gone at that stage.
If you are going to stay, let the other employer know asap so they can make other arrangements.