Hi Sam Andrews,
The table in this documentation page shows you what each of the Emerging Hot Spot Analysis patterns actually mean. You can imagine that many of these might change if a time step is missing - for example, a New Hot Spot is "A location that ... has never been a statistically significant hot spot before.". Perhaps this location was a hot spot in your missing year, hence this result might be wrong.
There isn't really a perfect solution but I see two options - one, as you suggested, simply acknowledge that there is a gap that could impact the results. Two, is to impute the values of the missing year with sensible values based on the values of neighboring years. I would do this by creating your 2006 features with null values, then filling these values using the Fill Missing Values tool with the Fill Method as Temporal Trend. This way you get an imputed value at each location for 2006 that adheres to the general trend of the values in each location.
Regards,
Lynne