This is a really great question and one that I have been asked on quite a few occasions. The short answer is absolutely yes, you can be submissive and not enjoy pain. There are even a number of groups on Fetlife for people who fall under this category and are often referred to as Sensual Submissives. For many people, being submissive is about the psychological aspect of giving up control to another person, rather than the physical. It's about playing with power dynamics, either in everyday life or often just within a sexual relationship.
Submission is often confused with pain play. Pain play is a specific form of kink play and is not a prerequisite to being submissive. In fact I know people who are not in the least bit submissive but still get off on receiving pain, so the two do not always go hand in hand.
It is a common misconception that spanking, impact play and other forms of pain play are required activities within a D/s relationship. Clearly the key is finding the right partner to explore with. Just as there are submissives who aren't into receiving pain there are many Dom(mes) who aren't into administering pain.
As I have said many times before, there is no right or wrong way to be submissive or in a D/s relationship. The only right way is the way that works best for you and your partner(s). The key is finding that partner, so don't be shy and tell your prospective Dom that pain play just isn't your thing. Open and honest communication about what you like (even if it's just an educated guess about what you might like) is the key, and anyone who says you are not a sub as a result has immediately eliminated themselves from your list of potential partners.