I have struggled with this issue since adolescence, long before I even became a Catholic just after college. My resounding answer to this question though is YES, it is quite possible. I am living proof.
Unfortunately Bipolar Disorder can have as a symptom engaging in unsafe sexual practices but that is neither an excuse nor a decision to merely accept promiscuity as a life choice.
Personally as a practicing Roman Catholic, I have access to the Eucharist and the Sacrament of Reconciliation to strengthen my resolve and heal myself if I were to stray from the "straight and narrow".
"Heal myself?" you may ask. All I mean is that God cannot work Wonders in anyone witout their consent or their "fiat" as I like to call it in my book. He respects us too much to violate our free will.
And yes, I understand that we as mere mortals do not possess absolute free will. It is conditional and can be lost due to sin.
Fortunately God walks with us and yes even carries us when we can no longer walk by ourselves.
He seeks us out. He finds us where we are and He patiently restores our will to live on one beautiful step at a time until we are running with joy into the arms of the Father.
Remember the story of the Prodigal Son? The father ran to meet and welcome back his wayward son. I like to think that later in that son's life he returned the gesture as he ran to be with and embrace his aging father. That's not biblical but just a happy and imaginative thought.
We are allowed to think. To imagine. To dream. As long as we don't confuse our dreams with reality and remember that God tells us that Heaven is beyond ANYTHING you can imagine. What a humbling thought. What a place to start the healing process anew.
Don't confuse sex with love.
Don't fall victim to the great lie of our age.
Chastity is possible even for the fallen.
We are not perfect on our own but united with Christ as His Body the Church we are wholly resurrected again yes here on Earth as in Heaven.
That is my opinion. That is my belief. That is my Faith. Lord have Mercy.