Yes, no, and maybe. Some roses ignor the hips relative to rebloom, and some are supposed to have less or no further blooming. You will probably have to take notes for each plant to answer your question for each plant.

Carol, if the rose in question is a modern HT, floribunda, climber or mini, it'll probably continue blooming. For those more closely related to species or OGRs, perhaps it might not. What rose, in particular, are you referring to? Kim

"In contrast, modern roses (hybrid tea, floribunda, and grandiflora cultivars) are repeat blooming and must be deadheaded to encourage continuous bloom."

The above is an example of a "rule" that is the opposite of a statement made in this thread. Which is right?

I suggest that both may be and that neither may be. Nature is complex. It may be another factor such as the length of daylight, amount of moisture, daytime heat, nighttime cold, amount of nitrogen available, whether a rose show is approaching, etc. that turns off flowering in place of the presence of hips and/or along with the presence of hips plus the ancestry of the particular rose.

Here is a link that might be useful: links with opposite rule

I was thinking of Night Owl and Memorial Day as seed parents. But now I'm thinking Night Owl (has a lot to offer) but I want a more fuller bloom on the offspring - so maybe I should go with Memorial Day and something else from my stable of roses. :)