The GPL License this theme links to explicitly states that:
You may copy and distribute verbatim copies of the Program’s source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty;
So no, you may not remove this notice.
If you perform your own original modifications, you should probably list bost authorship statements together. e.g.: "Original Primer WordPress theme by GoDaddy; Additional modifications [possibly, list them] by Darroosh."