Add an integration test. #8411

Job	Run time
1/4	14m 8s
2/4	12m 54s
3/4	12m 48s
4/4	13m 32s
py-3-latest	21m 25s
flaky	6m 11s
_remote_background_indep_poll	5m 8s
_remote_background_indep_tcp	7m 34s
macos 1/5	21m 17s
macos 2/5	24m 7s
codecov	11s
	2h 19m 15s

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