Yes you can but the statistical tests will be meaningless since they require a probability sample. See any statisics book to find out why this is so. David Booth
I don't think it would be a good idea to go for SEM. However, as mentioned by @Imran Anwar, PLS being a robust approach could be used to run the analysis. But @Shahul I am interested in knowing about the sample size and other sample representativeness attributes (other than normality); whether these criteria are fulfilled?