What are the issues when performing an ANCOVA with a covariate that is influenced by experimental manipulation? Context:
I am doing a study on lying.


*

*The independent variable was manipulated such that participants were either told to lie or tell the truth.

*The dependent variable is related to the amount of detail provided and is extracted from the text provided by participants(this is a standard system of deception detection called reality monitoring). 


Issue:
I noticed that much of the previous research (e.g., Sporer [2000]) has included or suggested the use of  word count as a covariate to make sure that any differences in the number of details do not simply reflect differences in the number of words. 
However, I was under the impression that covariates needed to be measured before the experimental manipulation and should not be related to the independent variable. 
Word count is measured after people have provided their truthful or deceptive account (And possibly related to truthfulness since people might provide more details by giving a longer account). I have read Miller and Chapman's paper on the misunderstanding of ANCOVA (FREE PDF). 
Questions


*

*Does including word count as a covariate looking at the effect of condition on details provided reduce statistical power?

*Is it meaningful to include a covariate that is measured after, and is assumed to be affected by, an experimental manipulation?

*How serious is violation of heterogeneity of covariance when including covariates?

*Rather than including word length as a covariate, often authors calculate number of details say per 100 words and then perform their analyses as normal. how is this different to including word length as a covariate?


Additional References:
For those interested, references include:


*

*Stromwall, L., & Granhag, A. (2005). Children's repeated lies and truths: effects on adults' judgements and reality monitoring scores. Psychiatry, Psychology and Law, 12(2), 345-356,  

*Vrij, A., Mann, S., Fisher, R., Leal, S., Milne, R., & Bull, R. (2008b). Increasing Cognitive Load to Facilitate Lie Detection: The Benefit of Recalling an Event in Reverse Order. Law and Human Behavior, 32(3), 253-265.

*Sporer, S. L. (2004). Reality monitoring and the detection of deception. In P. A. Granhag & L. Stromwall (Eds.), The detection of deception in forensic contexts. Cambridge: Cambridge University Press. 

 A: [Update / Note: Answer may be revised in light of ANCOVA questions.]
This is both an answer and a clarification.  It seems like the OP is asking about studying $\textrm{E}(NumDetails | (Honesty, NumWords))$ (so to speak), where $NumDetails$ is the # of details provided, $NumWords$ is the number of words used and $Honesty$ is 0 or 1, based on whether or not the person is telling the truth.  
In simple terms, the interest is on the conditional distribution (or expectation) of the number of details provided by the subject conditioned on both whether they are telling the truth and if they are particularly loquacious.
This is reasonable, but has a slight hitch: if loquaciousness is related to their honesty, then it may be helpful to find a relationship for that.  In any case, the number of details would generally have to be related to the number of words used to express the ideas.
To answer the basic question: It's not really so easy to say that it reduces power, because the question seems to be on the # of details, not on the detection of lying.
An implicit question is whether or not the number of words is a reasonable covariate.  It is.  It may be dependent on both the subject and the role they're asked to play.  You should investigate whether or not it has some dependence on the role (lying or honest), and, if the subject is measured repeatedly, the dependence on the subject.
With these in hand, you can address whether you get more details per, say, 100 words when they are lying versus when they are not.  You could stratify based on discrete intervals, such as 0-50 words, 51-100, etc. (or larger ranges), or based on quantiles (e.g. bottom quintile, 20-40%ile, and so on).  This way you may not need a formulaic model that estimates the distribution of # of words and # of details conditioned on the role and subject.
