engine oil in the coolant. Would a faulty lower intake manifold be the problem

These( 3.4 v-6 of this build era, do experience a disproportionate number of issues with this gasket. It may also be the head gasket , usually when failed this will leak externally as well at the corners of the intake, although exactly where is not defined. The gaskets are redesigned, the bolts will need to be changed as well and the proper methodology needs to be followed exactly. Failure to follow the repair procedure guidelines will result in more complications and issues in the future. Although when done correctly a gasket repair with the correct replacement parts and correct procedures will result in a lasting and quality repair. This is not a diy job for a beginner. If you have the skill set it is still not simple.