Since no one else has answered, I'll give it a shot.
The answer is no, you do not need to generate multiply imputed data nor use PROC MIANALYZE. There are several examples in the documentation for PROC SURVEYIMPUTE that demonstrate that you can use other survey procedures (such as SURVEYFREQ or SURVEYMEANS) directly on the imputed data. For example, see the Getting Started example: SAS Help Center: Getting Started: SURVEYIMPUTE Procedure
The doc provides several cautions about how to correctly analyze the imputed data. For example, in the Getting Started example, it states
Each row in the [original] data set represents an observation unit, but this is not true for the [imputed] data set. Therefore, it is very important to use only the weighted statistics from [the imputed data set].