If your interested in speed, look into a single-board computer with better data speed. The Pi 3B+ puts 100% of it's USB+Ethernet bandwidth through a single USB2.0 hub. This is why it's "gigabit" network is in theory limited to 300 Mb/s. In practice, since it shares that bandwidth with the USB, it can be much lower. Putting a USB drive on, and having the pi pull files off of it and push them out the network port would effectively halve that speed.
My recommendation would be a single board computer that has true Gigabit ethernet, and a USB 3.0 port. There are several out there, for not much more than the pi 3B+. Some with both of these features include the Odroid XU4 (I own one, and with 2GB ram and an octa core processor, it's quite speedy.) Also, there are several Allwinner H6 processor boards out there, and they have USB 3.0 and gigabit ethernet. The H6 based boards will be less expensive than the Odroid, but some have less ram, the CPU is quad-core, and software support can be a little more iffy. Not to say it's not a usable option, just do your research before you buy one.
On the original question: The setup that you describe would probably work fine. It would just be slow. The only issue that I could foresee would be if some USB 3.0 to SATA converters wouldn't work with USB 2.0, but the whole point of USB is the fact it's a Universal serial bus, and backwards compatibility at slower speeds is how every USB device I've ever seen works.