The short answer is 'yes' a internal blower can be removed and replaced with a downstream blower. A longer answer addressing your intended path includes what @User wrote above. In any case, start with the requirements for performance, estimate your pressure losses, and be sure that the in-line or external blower can pull the required volumetric flow rate at that pressure loss. Review many hood threads here for more information.

W.r.t. U-turn ducting and crawl space transit, attention to duct access for duct cleaning will be needed, or grease traps installed. The basic hood ventilation depends on baffles collecting part of the larger end of the grease particle spectrum and the blown-out warm rising air removing most of what is left. This mechanism is degraded when changing direction and having long horizontal sections.

Each 90º turn reduces pressure by as much as 50%.

Tim, I won't disagree with the others about your piping , but I bought a range hood online ( xtreme air ) that was terribly underpowered, but they did not accept returns without a huge restocking fee. I ended up removing the fan and installed a remote inline blower and a muffler, and am pretty happy with the results. One issue may be how to control the remote blower. One option is to wire the blower, and run a line to the wall near the range and install a speed controller. IIRC, i bought a speed controller from the same place I bought the blower, HVAC quick and did some surgery on the range hood, installed the control into the range hood, then redid the wiring of the hood so that it all worked. speed controls That took a lot of time, and wiring , since i wanted the light controls for the hood to also control the hood light.