If you recently finished a relationship you may tend to answer no, you are feeling down and unhappy with your situation. You have been raised to believe that happiness comes from achieving some goals, like find a good paying job, a good partner to share life with you and complete you. And when this things doesn't happen you may start to think that is something wrong with you.
The real answer to the question is it possible to be happy alone, is yes it is possible, because happiness is independent of you being alone or not, it doesn't matter what your relationship status is, in order for you to be happy.
Your essence is happy and it is perfect as it is and nothing can change that, no other person can diminish your essence.
But you live your life accordingly with your beliefs, if you truly believe that it takes one partner for you to be happy, then if you find yourself alone, you will feel that you no longer are happy. That is just a belief of yours, a belief is just a story and you are much more than your stories, you are the unlimited space where those stories happen.
Be aware of your beliefs and detach from them.
Beliefs are barriers that you build and limit your perception of your reality and as long as you believe in them you set aside all infinite possibilities out there for you to experience. Beliefs are filters that judge what is good and bad for you. They create expectations in you and when they don't come true you feel unlucky and unworthy.
Being aware of your essence you start loving reality as it is, nothing happens for no reason. And if it happens it is okay, otherwise it wouldn't happen. You can deal with whatever happens in your life, you may not like it sometimes, but you can deal with it and evolve from it.
Accepting reality as it is allows you to stop the war against what is, against life, because this war is a sure loss for you, the more you resist, more challenging situations will come until you give up and face reality as it is. You can't escape reality as it is. The only option for you is how long you will take to accept it.
And when you fully embrace reality as it is you realize that you already are all you could wish to be, nothing is lacking in you. No one can give you what you already have, be it love or happiness. It doesn't mean that relationships aren't necessary. Why they are necessary? Because they exist, the only difference is how you enter in a relationship.
You can be in a relationship from a needy situation, where you rely on your partner to make you happy, to complete you, be the other half. Or you can be in a relationship from a essence aligned situation, where you know that you need nothing and you want to share with your partner what you are and seize whatever life brings you both.