Assuming the chip card also has a magnetic stripe, then yes you can just use the stripe.
However, since magnetic stripes are pretty easy to counterfeit these days, if anyone challenges the charge you won't have a very strong defense. The card owner could tell their card company that it's a fraudulent transaction, and you may lose the money and have a negative mark against you without even being given a chance to defend the transaction as legitimate. Maybe.
Chips are much harder to counterfeit, so if the chip is inserted that almost certainly proves the real card was used to make the payment, which increases the liklihood that the card was being used by its owner. If someone were to claim the charge was fraudulent but the chip had been used, then the card company may be more likely to listen to your side of things (especially if the card owner never reported the card missing).
Also, magnetic stripes get damaged a lot. They wear out, get cracked, and sometimes demagnitized. If a customer's stripe won't work, you risk missing out on a sale. Happened to me at least once a month before I got my chip reader.
All that said, I'd say the odds of you being burned by only using the stripe is pretty low. You can probably just swipe forever and only have a handful of small issues per year.
