Not exactly. If a single user has 2 rows in the experiment assignment table, one mobile and one desktop, then they will be included twice in the dimension breakdown, once for each dimension value. So the total number of users if you add up the different dimensions will be greater than the total number of users on the overall results (no dimension selected).
However, the dimension doesn't flow through to metrics currently, which I think is what you wanted. So both times the user is included in the report, it will see all of their conversions. If they converted on mobile, it will also count as a conversion in the desktop dimension.