Suppose you have the following A record:

example.com. 3599 IN A 111.123.456.78

And these MX records:

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

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

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?