Yes, for the large part the computing work at Bell Labs was of a separate and distinct lineage from telephony. The story is somewhat complicated by AT&T's corporate history, as prior to divestiture AT&T was, for the most part, prohibited from selling "computers" as part of the terms of their regulated monopoly. In part as a result of this regulatory situation, the computing work at Bell Labs was viewed as more theoretical than applied. Telephone switching equipment itself, such as the ESS, never ran Unix. This is rather complicated by the fact that some sources (not incorrectly) describe the 5ESS as running UNIX, but in fact the so-called UNIX-RTR they ran was an independently developed operating system that featured partial UNIX compatibility. This was largely for convenience as by that time UNIX was often being used as a development and build environment for switching software.

It's easy to see why UNIX wasn't really involved in the telephone system itself: UNIX was designed as an operating system for mid and minicomputers such as the PDP that featured a largely "conventional" (from the modern perspective, the matter was less settled at the time) Von Neumann architecture with opportunistic scheduling. Telephone switches, back to the 1ESS and back to the XBAR if you choose to view it as a computing machine, tended to be Harvard architecture with real-time scheduling. This was viewed a far more suitable for telephone equipment since it had extremely high uptime and reliability requirements compared to computers. This comes from the different applications: in the '70s computers were still viewed as machines for offline processing in batch mode, where failures were handled by backing out and restarting the batch. Telephone switches were online machines that could not restart their work from the beginning without disrupting calls in progress. These were basically two completely separate lineages of computing machines that had little in common until the '90s, although the PDP itself was an important step in eroding that divide since it was popular for process control applications (this history relates to the reason the PDP was called the PDP).

Keep in mind as well that telephone switching equipment of that era made heavy use of hardware reliability measures (lockstep synchronization of redundant control modules and a large amount of "safety" logic implemented in hardware) as well as running almost entirely from read-only storage (in its most extreme form, the metal punchcards used by the 1ESS). These were further factors that made phone switches dissimilar enough from "computers" that they ran quite distinct software, which usually lacked many of the elements that we would now consider part of an "operating system" (e.g. dynamic process scheduling). To some extent this is still true although e.g. Nortel DMS is more often running off of RHEL-based controllers now.

General-purpose mainframes and minicomputers were heavily used within AT&T but for offline applications such as billing, accounting, and maintenance management. For example, many electronic exchange switches were originally paired with a PDP-11 class machine that tracked maintenance and fault data for the office to replace the original paper tickets. Over time these machines gained more capabilities such as automatic line testing, but they remained "external" to the phone switch for reliability reasons. Billing was, for the most part, done by physically removing the tapes from the switch's data recorder and loading it into a computer to totalize and generate bills. Later on this process was automated but still with a clear separation of the switching system and the billing system.

Post 1984 AT&T, no longer a regulated monopoly, was permitted to compete directly with IBM, Lexmark, etc with their computing division. The venture was an infamous failure, and AT&T never saw real traction as a computer vendor. AT&T's rapid technical development but failure to actually build a sustainable computer business is what brought us the UNIX ecosystem: they built it, but they couldn't sell it, so eventually they basically gave up and licensed it to anyone with a pulse.