Is it ethical? Sure, and it's done all the time (for real bridge reasons, see Joe's answer). It is not required to help declarer when it won't help partner.
What's not ethical is telling the opponents your signalling method, and then having it not be. "We play standard carding" is not the same as "we agreed standard carding but since my partner has the analysis skills of a wet fish, and wouldn't pay attention to my signals if I used a flare gun, my partner's signals are meaningless, and I lie about 50, 60% of the time", even if that has never been actually said (because of course it was never actually said).
Note that this is something that good opponents will figure out very quickly. Some will just go back to reading your "falsecards" better than your partner; some will call the TD after enough cases that it's not "Just Bridge" and force the issue; some will just bring it up to the TD after the round so that she is aware, can pay attention to it, and drop the hammer when she is convinced.
In certain jurisdictions (the ACBL is one), you are required to have a signalling method, you can not just say 'we play cards randomly'. This is because people don't ever 'play cards randomly', they play cards 'randomly' according to patterns, and those patterns do get worked out by their partner, even if they don't know they're doing it.
"We signal only when it's critical for partner to know it; when we do, it's right-side-up attitude or count" is fine; if it turns out that it's never critical for partner to know because partner doesn't look anyway, well.
In rubber bridge, things are different. First, you're playing with whoever you cut; second, everyone at the table has the same knowledge of your partner's ignoring them when they've cut your partner, to guess how accurate your signals are.