VerionOne does support ALM. It has been tested with HP-ALM versions 11.5, 12.0, and 12.2. Integration with older versions of HP-ALM may work, but are no longer supported by VersionOne.

Yes, a bidirectional integration will work seamlessly using an integration solution called OpsHub Integration Manager. You can checkout the HPALM VersionOne integration datasheet here. (https://www.opshub.com/versionone-integration/versionone-hpqc-integration/)

It supports following versions and entities of both systems:
HP ALM Versions: 10.0, 11.0 (Patch 8 i.e. HP ALM 11.00 Service Pack 3 and later), 11.5, 11.5x, 12.0, 12.2, 12.5, 12.52, 12.53 12.55

HP ALM Entities: Defect, Requirement, Test, Test Set, Test Run, Cycle (Supported in HPQC 11 and above), Release (Supported in HPQC 11 and above), Trigger Support, Test Set, Execution Request
VersionOne Versions: From 10.x up to 18.x

VersionOne Entities: Backlog Item, Defect, Epic, Goal, Issue, Request, Task, Test, TestSet, Theme, Project/Release, Iteration, Build Run, Changesets, Actuals