By way of comparison, Union conscription provided only 6 to 8 percent of all Union soldiers and the North never resorted to extending enlistments. The Union army could have faded away almost completely in the summer of 1864 when the 3 year enlistments ran out, and the fact that it didn't is a testament to the dedication of the Union soldier.
The Confederate draft didn’t bring a lot of draftees into the army. However, what the draft law DID do was stimulate volunteering. Many draft age southerners, faced with the draft, chose instead to volunteer. By volunteering, the men could choose their unit (usually a locally-raised one) and their branch of service (infantry, cavalry, artillery). Many regiments were raised in early 1862 of these late-coming volunteers.
The Union draft law operated somewhat the same way, with one twist. Many poor men who couldn’t afford the $300 to purchase an exemption formed what were essentially draft insurance pools, whereby 30 men would contribute $10 apiece to a pool so that if any of them was drafted, the pool could pay the $300 for the exemption. The government took the $300, and with the money raised could afford to pay those high enlistment bonuses that drew recruits.