The monthly seasonal indexes for a year should sum to 12. This is because the seasonal index for each month represents the average value of that month relative to the overall average for the year, and when you sum these relative indexes across all 12 months, the total reflects the annual cycle.
In the context of seasonal decomposition, if your indexes are expressed as relative values (e.g., percentages), they will still sum to a representation that reflects the total annual effect distributed across the months. Normally, when using a percentage format, the indexes will sum to 100 (if interpreted as a whole), but when working with seasonal indices directly related to the number of months, the sum will equal the number of months (12).
So, to answer your question: the monthly seasonal indexes will add up to 12.