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The control impact is small. It's most easily seen when flying time accelerated.
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Though I'm sure you are talking about a real effect, I can't help wondering if it reallly matters that much. Real-world aircraft wouldn't be expected to fly hands-off for long, and being perfectly trimmed for a shot is a rarity, so how does this affect anything of consequence? And come to that, I don't think any real-world contol system can have been totally error-free either: cable-operated systems are always prone to slackening, and even pushrod systems will have a degree of 'float' around neutral loading, unless they are artificially stiff.