If my memory doesn't fail me, Namecheap gives the option to either keep the same nameservers or switch to Namecheap's nameservers.

Unless you host your DNS externally (and you have GoDaddy configured to use those), you will have to switch to Namecheap's nameservers and I believe reconfigure your records.

For a smooth transition, you could change your nameserver configuration on GoDaddy before transferring, and then have Namecheap keep the settings.

EDIT: Just noticed another commenter mention that you can export your zones from GoDaddy.