IANAL. I just have some knowledge/experience.
A deposition about a work related issue may ask to see all devices that you use in connection with your employer. So yes, a deposition will care when you say you didn't use your personal phone for work if you can prove it by it not being on any device list found with work-related services.
A device list can be obtained (usually easily, sometimes with a court order) through many services you use. G Suite, Github, Microsoft Account, Slack, Reddit, etc... these all track what devices have logged into them with your account. Signal and Telegram have your phone number. And of course any email sent has a list of addresses to which it was sent. So make sure your personal devices aren't found to be communicating with coworkers or vendors and you'll have a valid argument for "I didn't use my personal device for work".
Whether it will stick will largely depend on how good the lawyers are because that's just one way your device can be in scope for a deposition. Another way would be if any messages from coworkers are sent to/from your personal email or phone number then that can also bring your devices into the scope of a deposition. It might depend on whether the content or context of the messages suggests that they're related to the subject of the deposition and that the conversation had been moved (eg, an attempt to hide it). Again, it largely depends on the quality of the lawyers involved.