Spoilerons will help kill lift if the airplane is slowed down enough. But if you increase the power and gain speed, the airplane will climb and can easily overpower the elevator. Same thing will happen as flaps, though the airplane goes down instead of up.
Not always, it does depend on the plane. factors like the CG location in relation to the flaperons and the tail moment have an effect. Planes with really short tail moments can almost act like flying wings, where raising spoilerons raises the nose and causes a climb as you say. While planes with a longer tail sometimes to go nose-down with the spoilerons up and nose-up with flaperons down. My combat planes are short-coupled with very short fuses, and I can and do trim the pitch by adjusting where the ailerons are at center. I "reflex" or raise both ailerons or lower them a bit to change the way the plane flys.
On the other hand, I have a Mossie that goes hard nose-up if the flaps are down and I'm going very fast. At very slow speeds, there's no noticeable pitch change at all. But adding power with flaps down gets an immediate nose-up. I had an old funfly plane years ago, I think it was called a tadpole, and it pitched up with flaperons down, which was desireable to help make really tight loops, control-line-flap style.