Has "管理 = manage" something to do with plumbing, making pipes or taking care of them?
No.
管理 is simply a modern combination of two related verbs for the Western concept of "management".
管, as a verb, carries a heavy connotation of restriction and setting rules.
理, as a verb, carries the meaning of intervening or acting.
As far as I know 管 is a measure word for tube-shaped objects.
No. 管 is either a noun or a verb. When it's a noun, it's the tube itself.
So my logic suggest that 管理 is an meaning-extension for managing pipe-works or running pipes, plumbing.
管 by itself does not carry the meaning of any pipe-works or running pipes. Water pipes are exactly expressed as 水管. Pipes (for utilities) or circular tunnels (transportation and escape routes) can be expressed as 管道.
Managing here is taken as a metaphore for guiding the "flow" in the desired direction.
Traditional Chinese philosophy of "management" suggests that good leaders should lead by example -- they should stick to the highest moral standards, and be kind to its people. It also concerns itself with law, order and inter-state relations. It does not, in any way, involve deciding directions, strategic planning or management by objectives.
Etymology of terms for modern concepts rarely deal with philosophy.
Modern Chinese likes disyllabic verb phrases for representing concepts (two verbs = one noun). Many of these translations are not accurate representations of the concept as a whole; many of them are terms borrowed from the Japanese after the Opium War.
A similar example is 責任 (responsibility), which is composed of characters meaning scold and appointment. The combination of words does not suggest that scold and appointment are the main ideas to responsibility.
尽管 "even though" has nothing to do with pipes either. 尽管 is one single morpheme; the two characters by themselves mean nothing related to the meaning of the whole phrase. The characters are simply borrowed for their pronunciation.
Similar examples include 什么 and 怎么 -- their meanings of "what" and "how" are not explainable by studying the meaning of the separate characters.
Terms related to 管理 and their meanings:
管理: to manage (by rules, procedures, regulations, strategies, etc).
处理: to handle, to process. 处理身后事 managing affairs (after death), 文书处理 word processing.
管治: to administer, to govern (as in governments governing people)
整理: to reorganize, as in cleaning up a messy room or desk, or organizing collected information (for a research project)
治理: to fix, usually something involving public health, public order or public utilities. 治理河道 river training.
整治: similar to the above, but with a more aggressive tone. May concern itself more with "correcting" bad trends.
整頓：similar to the above, but often directed towards industries. It carries the implication that a short-term (financial) loss would be incurred in exchange for long-term sustainability. 整頓旅遊業 suggests rooting out bad practices in the tourism industry.
管制：to regulate; to restrict. 利润管制 regulation of profits. 隧道管制區 Tunnel Control Area. 進出口管制 import/export restrictions. 排放管制 emission restrictions.
管束: to restrict, to hinder. Usually one party has authority over the other, i.e. parents over their kids.
