And even more, that we should embrace it and accept it (while at the same time avoiding the sufferings) ?
Many Mahayana Buddhist traditions believe that liberation is specifically freedom from suffering rather than freedom from being present in the universe.
But suffering is not to be avoided. It is to be prevented. The avoidance of suffering is what binds us to it. Recognising it's root causes and eliminating them is the journey to enlightenment.
This is why 'Right View' is so important within Buddhism. When we are able to see that the root cause of our misery is the mistaken view that sees permanence where there is none, sees joy where there is none, and sees self-existence where there is none, then our new view engages in a transvaluation of our experiences. Because of this transvaluation, our attitude towards some things will invariably change. For instance, we may look at a new car in a showroom - and just see it as a source of new trouble rather than as a source of joy.
So accepting and embracing the continuum of rebirth is to be encouraged; But to accept and embrace the unmodified, ignorant view of the transitory, empty, miserable shit-hole of the unenlightened state, and holding onto the idea that there is joy to be found in it - that's not a buddhist thing.
Embracing samsara and avoiding suffering is an oxymoron, since samsara equals suffering. Therefore it's impossible and goes against the four noble truths. If the definition of buddhism is adherence to the four noble truths, the answer to your question is no.
To complicate things, i am sceptic that buddhism teaches that we should liberate ourselves from samsara, but i'm probably getting caught in semantics now. My point is that buddhism says there's a way out of samsara, without imposing the noble eightfold path on people.
I don't think there are Buddhist schools that teach this explicitly.
There are some that say don't train for the cessation of suffering in this life, instead you can be a Buddha in some trillions of years, when you then pass away you go to the special Buddha heaven from where you can keep interacting with people stuck in Samsara for all of eternity.
Basically i don't think there is a school which would put it like this "our goal is to stay in samsara" but if one analyzes the doctrine it might turn out that their Dhamma is counterfeit and doesn't lead to liberation because it's closer to sci-fi than reality, complete with impossible worlds, a soul and other unforunate ideas of how things work.
The entirety of Buddhist teaching is about how one can achieve long-lasting happiness. No Buddhist school teaches that we MUST get liberated from suffering. But IF you want to get liberated, THEN Buddhism offers a path. If one has already achieved long lasting happiness, then there is no need of Buddhism. Similarly, if one does not want to end one's suffering, then there is no need of BUddhism. To talk of samsaric cycle, is to talk about the endless cycle of suffering. To come out of the ednless cycle is synonymous to ending suffering. Buddhism, taught out of compassion, will always teach about how one CAN come out of the endless samsaric cycle.