In brief, the answer to your first question is "yes", and a reformulated version of your second question has answer "conjecturally, yes".
For the first, more precisely, Eisenstein series formed with automorphic cuspidal repns as inducing data appear in the spectral decomposition of larger GL(n)s.
For the second, it is part of Langlands' conjectures that all the L-functions for all reductive groups appear as standard L-functions for suitable GL(n). Not the literal automorphic functions or repns, but the "data" in a suitable sense.
There is a lot more that can be said...