Can non-alcoholic beer give a positive EtG test?

It can. There are two studies involving NA beer: Thierauf 2010 (http://www.sciencedirect.com/science/article/pii/S0379073810002094) and Musshoff 2008 (http://www.ncbi.nlm.nih.gov/pubmed/20838803)

Some NA beers still contain .5% alcohol. You can search for those with no alcohol but it still is iffy when it comes to an EtG test. You can drink orange juice and test positive on an EtG, they are that reliable.