Using internet recovery to install Mac OS X on SSHD, then replace internal?
Yes. OS X supports external bootable volumes fine, and doesn't differentiate in any meaningful way between an external and internal bootable volume.

I would recommend using Migration Assistant to migrate your files, however, if possible–but you'd need a second Mac for this. A relatively easy workaround is to simply "restore" the external disk using the internal disk as the source. You'll need to first boot onto an external drive of some sort or Internet Recovery (assuming your Mac is new enough) (to my knowledge, the recovery partition won't work), then use Disk Utility from there.


Select the external volume in the sidebar, then select Edit > Restore.
Click the Restore pop-up menu, then choose the internal volume.
Click Restore, then click Done.