Yes - when I worked with a large bank, delivery teams used Jira for work management and dates from the release burnup chart in Jira were used by PMs supporting those teams to create and track schedules (higher level) in MSP.
At my last company, the developers and BAs used Jira to track their work and their time, and to manage releases. The PMs on non-agile projects used MS Project for Gantt charts, tracking dependencies, forecasting, etc... We used scrum and kanban boards for agile projects.
We didn't have any integrations in place, for sharing information between systems.
MS Project had been in use for years; Jira was a more recent adoption, specifically for the purpose of tracking developer work and time - there was a lot they did that was not part of a project. There wasn't a lot of effort put into identifying extensions that mirrored MS Project functionality.
We had tried a system that was supposed to work for both work/time tracking and project management (EPM Live), but we tried to do more with it than it was capable of and it ended up not being usable - it probably would have been a good tool otherwise. Saving Changes...
Yes I have seen the two used together but not very successfully. Pick one or the other would be my advice.
Jira is great for project collaboration, managing a backlog and iteration planning. If you are already using Jira for project collaboration I suspect there is not much that MS Project can add other than smarter Gantt charts and critical path analysis. Jira is probably most popular with software development teams however and Gantt charts and critical path analysis tend to be worse than useless for software development. Saving Changes...
Using both didn't work in my organization, we moved to Workfront. Workfront allow an integration between Jira and the more traditional project plans. Saving Changes...