Maybe there can be a link between missing data and reliability (Cronbach's alpha) as missingness would reduce the sample size, however there is no evidence that N is related to alpha.
Also, in the process of scale development missingness at an item level is often used as an indication that the item is difficult to understand (maybe too cognitively demanding or just worded poorly in a confusing way). I suspect that such items would be responded to in a more 'random' fashion, thereby introducing more measurement error, and thereby reducing reliability.
Thinking generally, and without too much consideration (it's still early in the morning), I suppose that missingingness is very rarely considered to be reflecting 'good' measurement. Quite the reverse, missingness is generally considered to be indicative of measurement problems and so, if pressed for an answer, I'd say that missingness (usually, generally, in most cases, .... and all other caveats) would be associated with lower reliability.
The percentage of missing values should not be over 5%. If this percentage is exceeded, the researcher should seek for the reasons why the sample chooses not to answer this question and therefore a redesign of the research tool should be attempted.