Nipple Stimulation & Breastmilk

So I'm having a medical induction on Tuesday and my doctor gave me permission to try to induce labor on my own so I don't have to have pitocin and be restrained by monitors during delivery. Although, he doesn't feel anything TRULY works, he said it was fine to try whatever. He suggested nipple stimulation as the most likely to help. 
My question is, if I try to use my breast pump, will milk/colostrum actually come out? What if it does? Do I bring it to the hospital with me or leave it in my fridge? I don't feel like my breasts are full by any means so I'm wondering if my milk has even come in yet.. any advice is welcome because I really have no clue what to expect!

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