I have a bunch of slips still growing out of the actual tuber. If I keep them in the house and treat them as a regular plant over winter, can I pull the slips to plant in spring and will they produce as if they were fresh sprouted slips?
I'm not sure your sweet potato slips will survive all winter attached to just the tuber. I would either pull off long slips and root them in pots using rooting hormone or I would put the tuber they are attached to into a pot or tray of soil, partially covered with dirt so it can put out roots to get nutrients and water. Cover it with a bag to hold in humidity until it is well rooted.
In the spring you can take cuttings and plant them out.
If you're not familiar with propagating by cuttings I'm sure you can find instructions online or in gardening books.
I've done this with the ornamental sweet potato vines.