I had a hard time finding use rates of contraceptives among women of child-bearing age (15-49), but I found it for four years. Then I found how many women there were of child-bearing age that year and the number of abortions performed that year. Here's the numbers. You can make your own conclusions, or you can read mine. I cited the sources for my numbers below as well, so feel free to double check. I used LibreOffice Calc to automatically calculate the percent of women who had an abortion, but feel free to double check those numbers if you wish as well.
While I hated statistics in college, I'm seeing that from the numbers I found, every year, except the first year that abortion was legalized, that the higher the rate of the use of contraceptive, the higher the rate of abortion among women of child-bearing age. So my conclusion would be that yes, in fact, higher contraceptive use correlates with a higher abortion rate.
Sources:
Abortions per year: http://www.johnstonsarchive.net/policy/abortion/graphusabrate.html (They pulled their abortion numbers from a couple places on http://www.guttmacher.org/. I used them because it had it all in one place versus several different pages)
Population of Women of Child-bearing Age 1973, 1976: http://www.cdc.gov/nchs/data/statab/pop6097.pdf
Population of Women of Child-bearing Age 1995: http://www.census.gov/popest/data/national/totals/1990s/tables/nat-agesex.txt
Population of Women of Child-bearing Age 2006: https://www.census.gov/population/age/data/2006comp.html Table 1.1
Percent of Women using Contraceptives 1973, 1976: http://www.cdc.gov/nchs/data/series/sr_23/sr23_010.pdf
Percent of Women using Contraceptives 1995, 2006: http://www.cdc.gov/nchs/data/series/sr_23/sr23_029.pdf
