I'm pretty sure that DP is required in order to take advantage of the full features of the PG278Q (gsync and 144Hz). You would need an expensive DP to dual-link dvi adapter. Is there some reason you cannot simply connect DP directly?
I think I misunderstood your original question. I didn't realize that DVI to DP adapters existed. It is unlikely that they would be able to work if they existed. DVI already does not have enough bandwidth and running it through an active adapter would only lower the bandwidth.