Nope. IQ is negatively correlated with most mental illness. It is certainly not positively correlated with schizophrenia: https://www.gwern.net/iq
I am by no means saying that the underlying traits are casually related — only that metrics which predict one may also predict the other.
The human brain is a complex system and IQ itself is a very simplistic way to characterize it.
Think of it this way: imagine IQ is like electricity powering a city. Different city configurations have very different power and load requirements. You might find that, in general, cities with more power function better.
But perhaps the well functioning cities also had better transmission infrastructure. If you applied the rule of “more power is better” to a city without that infrastructure it would blow fuses everywhere and cause chaos.
With this example aside, In fact the science does say that there is a relationship: https://www.nature.com/articles/s41380-018-0332-x?WT.feed_na...
As it turns out, we have multiple contradictory findings about whether high IQ is positively or negatively correlated with mental illness.
But even if you believe there's a negative correlation, it doesn't mean that many predictive SNPs can't predict both.
E.g. cloud cover is predictive both for rainfall and heavy snow. However, heavy snow is negatively correlated with rainfall. The latter doesn't negate the former.