The questions in your title and body are different in a rather significant way.
In answer to "Could removing outliers be called cherrypicking data?": yes, of course it could.
In answer to "Would it be called cherrypicking data?", that depends on your justification (and apparent motivation).
To be honest I would generally be very suspicious of any paper which removed data points without a very clear and justifiable reason. It isn't possible to tell whether that's the case for your example, as you haven't given any information on it, and additionally for statistical advice it would be more appropriate to ask this over at Cross-Validated.
There are statistical methods for identifying how much of an outlier a point is (leverage, for example) but they are not in and of themselves sufficient justification for removing a point.
 thanks for adding more information to your question. Firstly, it's great that you haven't started collecting data yet, and well done for thinking about this at this stage. As @penguin-knight suggests, formulate a protocol for data collection and identifying suspect data before you start (a priori). However, do remember that the only defensible reason for removing an outlying data point is because you believe it is inaccurate and reflects a problem with how that sample was generated or quantified.
Secondly, regarding the ANOVA part of your question: one of the assumptions when using an ANOVA is that your residuals are normally distributed. 'Outliers' may indicate that this assumption is incorrect. If this is the case, simply ignoring some points is not the correct way to deal with this. Your simplest options are: