Suppose you have the following A record:

    example.com. 3599 IN A 192.0.2.78

And these MX records:

    example.com. 997 IN MX 10 mx01.1and1.co.uk.example.
    example.com. 997 IN MX 10 mx00.1and1.co.uk.example.

And you then changed the IP address for the A record to a non 1&1 ip address (so that the website could be hosted on an external hosting), would that affect the MX records or mess up the email in any way?