Lets say a wormhole exists with point A inside the gravity well of a star and point B in a space where there is no notable nearby mass to create a gravitational force. If one were to approach point B, would one experience gravity from the star near point A of the wormhole? Do gravitational effects 'travel' through a wormhole?
First let me say that wormholes, event horizons and many other possible effects associated with collapsed stars are currently purely theoretical. We think these effects and other associated events may result from the collapse of a star with a mass in excess of the Chandrasekhar Limit
We are fairly sure we are on the right track as to what what those effects are because we use GR to predict them, and it is a theory that, so far at least, has passed every test we have thrown at it.
Unfortunately we have as yet no direct proof of these exotic effects, and experts in General Relativity (and I am NOT one of them) may sometimes disagree about the detailed physics of black holes.
Any ideas about wormholes allowing you to move to another universe, or different places within our universe, are currently predictions using the math of GR , some of which may well be correct but none of which we have any proof of, as of today.
General Relativity has been confirmed very well in "normal" situations, such as predicting the changes in orbit of Mercury, and we use it's predicted effects in GPS systems, but when it comes to extreme events, such as black holes, we are predicting what "might" happen, more than currently observing what is actually happening.
If a wormhole exists in the gravity well of a star is the same as saying, if a blackhole singularity "appears" near a star.
Well, the first thing that will probably happen is that the black hole will pull the normal star towards it, possibly creating what is called an accretion disc of material from the other star.
We are pretty sure we have evidence that this actually happens. In the worse case (for the normal star), it will be pulled apart by the intense gravity of the black hole.
Anything located at point B, will feel the effects of the black hole, and a wormhole (if such a thing actually exists) will affect anything at point B, just like a normal star would, there may not be anything much exotic about it, just ordinary gravity.
So , in that sense, will the gravity effects travel through the wormhole, is the same as saying point B feels the effects of gravity.
The "wormhole", that is the point of intense gravity, will act in exactly the same way as the Sun pulls the Earth towards it.