Combined merging and pushing
It is possible to do both, merging and pushing between a mainline project and a branch.
However in that case you need to carefully choose the last synchronization point: either the last merge or the last push operation, as it cannot be automatically chosen depending on what you want.
If you are unsure which date/time to pick you can simulate the merge or push and review the changes beforehand by just executing only the first steps of the merge/push wizard.