Majority of OMPs are indeed beta-barrels, but there are (very few) examples of helical proteins as well. See for example this entry in Orientations of Proteins in Membranes Database.

Solving structures of membrane proteins is not that easy, so I'd say we haven't sampled structural variability of membrane proteome yet.

If you want to just have an eyeball, I recently created an image gallery for a pretty comprehensive bunch of structures of membrane proteins.

You can address this question using the advanced search interface at the Protein Data Bank. As the PDB has an API, I imagine there's also a programmatic solution.

You might get started as follows:

1. Select secondary structure content as a query and specify a minimum of 1 alpha helix
2. Click "add search criteria"
3. Select cell component browser (GO), search for "outer membrane" and add the appropriate GO term, e.g. cell outer membrane GO ID:9279
4. Submit query

The parameters described above return about 204 results. Many of these are predominantly beta-barrel. The query can be refined by specifying minimum/maximum number or percentage content of alpha-helix and beta sheet. Specifying minimum 50% alpha-helix, for example, currently returns 27 results.

The Stephen White lab keeps a constantly updated tab on membrane proteins of known structure on this page.

Apparently the answer is yes, there are at least 3. If you go down to the Transmembrane Proteins: Alpha-Helical > Outer Membrane Proteins section you will see these 3:

1. Wza translocon for capsular polysaccharides: Escherichia coli, 2.25 Å
2. Porin B monomer: Corynebacterium glutamicum (expressed in Escherichia coli), 1.82 Å
3. Type IV outer membrane secretion complex: Escherichia coli, 2.60 Å

This link brings you to that section of the page.

See also TMPad

The TransMembrane Protein Helix-Packing Database (TMPad) is an integrated repository of experimentally determined structural folds derived from helix-helix interactions in alpha-helical membrane proteins.