Yes. Predestination most certainly and infallibly takes effect, yet it does not impose any necessity (so that its effect should take place from necessity) because predestination is a part of providence (and the order of providence is infallible) but not all things subject to providence are necessary.
The order of predestination is certain, yet free-will is not destroyed; whence the effect of predestination has its contingency.
The divine knowledge and will do not destroy contingency in things, although they themselves are most certain and infallible.
And God does not permit some to fall, without raising others.