Not likely. The 1x7 devices appear to have undergone a major design change. The 1x5 and 1x6 devices were built on Intel network controllers. The 1x7 devices have a Marvell switch (which, incidentally, shows in your lspci listing). That switch operates as a router unto itself (it has its own ARM processor), and the main device must be able to give it explicit operating instructions.
Netgate has a device incorporating a Marvell switch (the 7100, I believe), and they had to write a whole bunch of new code to make the switch work with pfSense Plus. That code was specific to one particular model in the Prestera family of switches and exists only within the proprietary pfSense Plus and not in the open-source pfSense CE.
One time I have encountered a similar switch before was on a Barracuda F180 (see this thread). On that occasion, it turned out that absent explicit direction, the switch works as a dumb switch (i.e., as if it were a single Ethernet port with an external dumb switch connected to it). The F180, however, has other ports in addition to those in the switch, so this is workable. In your case, when all available ports are in the switch, I doubt it is possible to make the router work properly without a driver for the switch. And I am not aware of any such driver forthcoming. I'd love to be wrong on this, but I don't think I am...