Possible: yes. Unlikely though.
Assumptions: 3½ inch drives usually need more power than you can provide by USB. To solve that it might be possible to cluster a dozen USB cables and some complex logic, but an external PSU is way more common.
And assuming an external PSU is the case for your setup it is unlikely that they spent extra resources on making it able to use power from the USB bus in case that someone put in a non-standard drive (2½" drives in 3½" enclosure is not standard) and wanted to use that without PSU.
So, basically it is very unlikely to work since the external case now only legally has access to 1 bin of power (100mW @ 5v for USB2, 150mW for USB3 IIRC).
I write 'legally' since many USB implementations still offer more power even if the device did not ask for more then the starting 1 bin of power. Which means drawing more power over circuits which do not have to be capable to handle that. Still, un an unlikely case it could be made to work.
Practical answer though: No.
. But likely you would need to change some wiring and hope that the USB connection offers enough power to run the drive and electronics even if the external logic