If James Baxter gives me a Creeper can I discard it
If you look at the text on the card you will notice that the instructions are broken up into 3 sections. What this says to me is that first everyone will draw a card and if they get a creeper they will put it into play and draw a replacement card. Once everyone has drawn the card the next section will happen which causes all creepers in play to be discarded. So that will mean any creeper that is drawn as part of this action will also be discarded as part of this action.
If the action was not to discard the creepers already in play it most likely would have come before the draw step or would have been included in the wording of the draw step.

All Players draw a card.
All Creepers in play are immediately discarded
All Hand and Keeper Limit Rules are immediately discarded

Text came from a picture on this site