Yes — and it’s not as uncommon as it might seem. Even after a round played better than your current Handicap Index, the Index may still go up.
Remember that your Handicap Index is calculated based on your most recent 20 scores. Each new score enters the record, and the oldest of the 20 drops out.
So, if your latest round is good but not as good as the oldest score being replaced, your Handicap Index can actually increase.