for polygons? Sure, that's easy.
Select both objects and Polygons > Combine. Then select the vertices you want to merge and Edit Polygons > Merge Vertices. In the Merge Vertices options, you'll probably need to adjust the distance slider to determine how close the vertices can be to each other in order to merge.
What I usually do is point snap the vertices I want to merge together, then merge them with a very low distance, like .0001.
Hope that works for you.