Yes, it globally shortens the gearing. There is better acceleration with a shorter FD, but only as long as you are in the same gear with each setup. Here's why.

Acceleration is a function of torque at the wheels, which is torque at the crank times gearing (less drivetrain losses). Most of our cars have a relatively flat torque curve, so where you are in the revband doesn't matter as much as how much gearing you have. In a nutshell - if you have shorter overall gearing, you have faster acceleration. So your point is correct, that shorter gearing means that the car accelerates faster... as long as you can remain in the same gear. However, as soon as the shorter gearing forces you to upshift, you are at a disadvantage because your overall gearing is actually longer.

For example, let's use the ITR as an example, with stock size (195/55-15) tires, taking deflection into account, assume we will accelerate to the 8400 RPM stock redline, and compare the stock gears with the stock FD (4.4) vs the ATS FD (4.928). We can calculate the total gearing (ratios of each of the regular five-speed gears times the ratio of the FD) at various road speeds. This will tell us which FD gives better acceleration, as follows:

0-35.6 mph: Stock FD first gear total gearing 14.21, ATS FD first gear total gearing 15.92, ATS is quicker (12 percent gearing advantage)

35.6-39.9 mph: Stock FD first gear total gearing 14.21, ATS FD second gear total gearing 10.37, Stock is quicker (37 percent gearing advantage)

39.9-54.7 mph: Stock FD second gear total gearing 9.26, ATS FD second gear total gearing 10.37, ATS is quicker (12 percent gearing advantage)

54.7-61.2 mph: Stock FD second gear total gearing 9.26, ATS FD third gear total gearing 7.19, Stock is quicker (29 percent gearing advantage)

61.2-78.9 mph: Stock FD third gear total gearing 6.42, ATS FD third gear total gearing 7.19, ATS is quicker (12 percent gearing advantage)

78.9-88.4 mph: Stock FD third gear total gearing 6.42, ATS FD fourth gear total gearing 5.46, Stock is quicker (18 percent gearing advantage)

88.4-104.0 mph: Stock FD fourth gear total gearing 4.87, ATS FD fourth gear total gearing 5.46, ATS is quicker (12 percent gearing advantage)

104.0-116.5 mph: Stock FD fourth gear total gearing 4.87, ATS FD fifth gear total gearing 4.18, Stock is quicker (17 percent gearing advantage)

116.5-135.7 mph: Stock FD fifth gear total gearing 3.73, ATS FD fifth gear total gearing 4.18, ATS is quicker (12 percent gearing advantage)

135.7-152.0 mph: Stock FD fifth gear total gearing 3.73, ATS FD exceeds redline, Stock is quicker

As you can see, when both FD ratios put you in the same gear with either setup, the shorter FD is faster. But at speeds where the shorter FD puts you into a higher gear, the stock FD is faster - considerably faster.

This is why the stock FD can be a big advantage on tracks where you spend a lot of time near redline, but the shorter FD can be a big advantage on tracks where you don't. So theoretically, if you were on a track where you spent the entire track driving between 79 and 88 mph, or between 88 and 104 mph, you would have a clear cut winner between the two gearing setups. However, most tracks have enough of a mix of speeds that you're probably going to be spending some time in the same gear, and some time in the higher gear, and the gains in one set of stretches will largely offset the losses in others.

On a dragstrip, OTOH, the shorter FD is more consistently an advantage, because of the large amount of time you would be in first gear, and in second gear, with either setup. In our ITR example, from 0 to 55 mph, the shorter FD is a significant advantage most of the time; however, above 55 mph (where you spend road course time) the advantage swaps back and forth between the two setups, depending on the road speed.

That's a long answer to a short question, I know...