You can, but typically you don't want the starter wort in your actual batch because the flavors that develop as a result of vigorous yeast growth typically aren't quite desirable in an actual batch of beer. You can make your starter in your carboy, but you will want to decant off the starter wort while keeping the yeast. The easiest way to separate yeast from wort is to refrigerate, and if you can fit a whole carboy in your fridge, you've got one heck of a tolerant woman backing you up, so good on you.
Good luck bud
Gypsy Head Brewing Company
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