Can teething make my baby's sleep restless?

You betcha. Teething is slightly painful. The teeth are cutting up through the gum tissue, and this is a new sensation for your baby. As i'm sure you can imagine, any time a baby is in pain, they won't sleep well.
Yes. Some babies can have decreased sleep due to teething. This is often more noticeable when the teeth are getting ready to erupt through the gum lines. If the pain is severe enough to cause your baby to cry and interrupt sleep, try a dose of Acetaminophen (ibuprofen is also very good for infants 6 months of age and older). Teething toys are also very soothing to many infants.