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Sure it would. It would just not be the traditional color selection. Log cabin refers to a construction method / family of blocks, more than any one specific quilt pattern.
I've read that the use of red in the centers was very much a practical consideration. Reds, though prized, were in shorter supply than the duller, drab colors which were scraps from clothing. So the clever quilters used those small bright bits as centers of log cabin blocks, recognizing that they would thus ensure that the prized red was evenly distributed throughout the quilt.
RST