Yes, if you have a multinomial response with complex survey data then you should use Proc SURVEYLOGISTIC. If it is an ordinal response then you simply need the usual MODEL statement and it will fit a proportional odds model by default. If you want to fit a generalized logit model then you will also need to place the LINK=GLOGIT on the MODEL statement as well.
Currently, the only available goodness-of-fit tests in PROC SURVEYLOGISTIC are found in the default output under the title "Testing Global Null Hypothesis: BETA=0". This is a general limitation with logit models on complex survey data, in that very few measures to assess fit have been defined. You could compute raw residuals, but for a logit model these are not usually very helpful. For now, all that is available are the ones I mentioned along with the c-statistic.
The Hosmer-Lemeshow test, for example, has been shown to be inappropriate in complex sample designs. This is discussed in "Testing Goodness-Of-Fit for Logistic Regression with Survey Data" by Graubard, Korn and Midthune.
Graubard, B.I., Korn, E.L., Midthune, D., 1997. Testing goodness-of-fit for logistic regression with survey data. In: Proceedings of the Section on Survey Research Methods.American Statistical Association,
