I would not expect better germination from a culvert pipe type cultipacker than you get from ATV tires. I think it just speeds the process by allowing you to cover more ground with each pass. You might see some benefit over both with a farm culitpacker. In addition to pressing seed into the soil for better seed soil contact, a farm type cultipacker puts an uneven surface on the soil with either V wheels that put small trenches in the soil or toothed wheels that put dimples in the soil. This can help, depending on topography of the field, by holding rain and allowing it to soak in rather than run off.
Regardless of how you do it, I find that the biggest improvement comes from rolling anything over the seed rather than just broadcasting it and letting nature take its course. Depending on the seed, I've seen a small improvement in germination if I get a good rain to beat it in and splash soil on it, to a big improvement if I don't get rain for a bit.
Thanks,
Jack