Do W's show up on home institution's transcript from a community college?

This summer I initially signed up for two summer classes at my home’s local community college, as a visiting student, to transfer credit to the college I go to(an out of state flagship state school). I withdrew from one of the classes within the first week and took a W. The other class I’ll get an A in. I know that for the college I go to, you have to have a D- or above to receive credit.

So, my question is, will the W show up on the transcript on where I am a full time student at once I send my transcript over?

You need to ask them. In many cases, the only transferred-in credits will appear.