I don't see why it wouldn't work.
Consider a tool such as an impact wrench. Most of those are rated for avg consumption of 5-7 scfm @ 90. Average is generally assuming 25% duty cycle, so while the tool is actually running it's consuming 20-32 scfm, all moving through that 3/8" hose. If your concern is the oil falling out of the air, reconsider the velocity with which that air must be moving to get that much air through that small of a hose. I'd need measurements of the actual pressure and flow during operation to calculate that velocity, but off the top of my head, I would imagine it in the hundreds of feet per second. Sufficient to carry a meaningful quantity of oil along with it.
That said, if I had an automatic oiler, I'd still oil my tools manually also. Mine get oiled before they get put away at the end of the day. That way, if they've gotten wet during use, at least they are put away freshly oiled to avoid corrosion.
I read an article a while back on shop air plumbing. It actually recommended manual tool oiling even with an automatic oiler. The comment they made, was that the purpose of the air line oiler, was not to oil the air tools, but the air LINES, which makes sense if your air distribution lines are black iron pipe.
What also may make the difference is where the oiler is installed. At the compressor, prior to the distribution lines, I think would get less oil out to the air tool than an oiler installed at the point where the individual air hose begins.