TBN is merely a measure of an oil's ability to neutralize and/or buffering capability insofar as it relates to combustion gasses. Obviously you would not want highly acidic oil circulating in your crankcase, eating away your metallic parts and gaskets.
Sludge is invariably caused by localized thermal breakdown of oil, due to factors including localized heating, poor circulation of oil, overly 'thick' oil, and oil with an inadequate flashpoint for the particular application.
For example, sludge buildup is seen when oil that has experienced drastic viscosity thickening is run. The reasons for the sludge buildup are as follows:
a) The 'thick' oil doesn't cool the engine effectively, so the engine runs hotter. Thick oil also can't be pumped through the engine at nearly the same rate as thinner oil can.
b) The hotter running engine therefore experiences higher surface temperatures internally, which in turn, causes some poorly circulated oil to be overheated.
c) The overheated oil forms as sludge on the innards of the engine and in the oil, further thickening the oil, further making the problem in a) worse, and the cycle repeats.
Reciprocating engine oil is unique in that it is formulated to be extremely basic, as compared to turbine oils that do not need to be formulated with basic neutralizers. Turbine oils and gear oils therefore will have fairly low TBN's as they are not exposed to combustion gases.
To answer the original questions:
1) Yes, a used oil analysis will measure viscosity thickening. If the oil has thickened to a high degree, ie: a 5W30 thickens into a 20W50 grade, it is likely that some sludge formation has occurred.
2) TBN is generally represented in terms of a sodium hydroxide (NaOH) titration equivilant. Sodium hydroxide, or bases in general, are generally good dissolvers of organic material, such as sludge, while acids are good dissolvers of metallic components. A weak TBN not only shows that the oil has been depleted through combustion gas acid loading, but also shows depletion due to reaction with carbon-laden deposits or thermal breakdown products of oil itself.