I'd be glad to be proven wrong but I don't think it's directly possible; I wasn't able to find any way (nor any information on how) to do that directly myself.
The way we worked around it was by creating a custom field in Jira (calling it 'Ticket status') and mapping it via inbound mapping to 'Status' field in Zendesk.
We then execute the queries in Jira against the local field.
it might be obvious for you, but can you please tell me how can I set this field automatically. I do have connection from Zendesk to Jira, and I do have the ticket status in both, but the idea is to have a quick filter to filter the existing bugs that have connections to some zendesk tickets. So the idea is to use either this custom field or some existing jira+zendesk functionality in JQL filters.
I think I found an easier way to query issues with JQL. Zendesk adds a label to any issue which is created from or linked to from Zendesk. So, you can search for "labels = jira_escalated". This at least gives you the list of issues in JIRA from Zendesk so you can look at the Zendesk status when you open the issue.
May be too simplistic for what you want to do, but thought it might help.
Assuming that you use 'CustomWare Zendesk Connector Plugin' and have your connection with Zendesk already working, you enter admin mode and go to Plugins > Mappings.
Find the right connection in the 'View Mappings' screen and click 'Configure' next to it. This will reveal 'Configure Mappings' screen - there, you're looking for section 'Add Field Mapping' which will allow you to map Zendesk's 'Status' your new field in JIRA. Remember to set correct 'Direction' parameter.
As a side note - I have my 'Ticket status' field configured in JIRA as a 'Select List' with values corresponding to ticket statuses in Zendesk: New, Open, Pending, Solved (I haven't tried mapping to a free text field in JIRA but I assume it should work too). When configuring your field in JIRA make sure to set a 'Searcher' for it (in my case it's 'Select List Searcher') so that it can be used in queries.
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