It depends a lot on your company, so I think your inside view will be better than our outside view. I told my employer when I went out to do a tryout with CFAR, and that went well. One reason I told my boss was that, if I were hired, I'd need to scramble to get all my projects annotated well enough to be able to pass of seamlessly, and I didn't want her to be left in the lurch or to make any plans that hinged on having her quant around for the next month. (Hiring sometimes took a while at my old company).

My boss really appreciated my being forthright and it saved me a lot of tsuris. I think it also worked better because it was expected that people in my role (Research Associate) wouldn't stick around forever.

It is only deceitful if you haven't made a honest effort to improve your situation in your current company. It is as deceitful to stay silent and don't give your employer a chance to increase your salary of your position.

It depends on the type of company of course. There are those that see you as an exchangable human resource where it may be appropriate to see the company as a slave owner who has to be hidden tghe truth of your escape from.

But there are companies where honesty about work situations is seen as interest in the company and critique used as feedback to improve the environment.

Salary negotiatons will be always tough though. Strictly comparing offers is the only reliable way to sell yourself. Everything else is falling prey to the salary negotiation tricks of the business world.

EDIT: I'm from Germany so my view my be country specific.

How bad an idea would it be to just let my employer know what's going on?

Extremely bad. People have been fired or denied promotion because of this. Don't even tell any of your colleagues.

I am not discussing the legal aspects of this, but you will probably be perceived as not worth investing in the long term. Imagine that your interview fails and you decide to stay. Your current employer is not going to trust you with anything important anymore, because they will be expecting you to leave soon anyway.

Okay, this may sound irrational, because you are not your employer's slave, and technically you are (any anyone else is) free to leave sooner or later. But people still make estimates. It is in your best interest to pretend to be a loyal and motivated employee, until the day you are 100% ready to leave.

It feels deceitful

This is part of the human nature; what we have evolved to do. Even your dislike for deceit is part of the deceit mechanism. If you unilaterally decide to stop playing the game, it most likely means you lose.

There is probably an article by Robin Hanson about how LinkedIn helps us to get in contact with new job offers while maintaining plausible deniability, which is what makes it so popular, but I can't find the link now.

I'm not ready for my current employer to know about this, so I've created a throwaway account to ask about it.

A week ago I interviewed with Google, and I just got the feedback: they're very happy and want to move forward. They've sent me an email asking for various details, including my current salary.

Now it seems to me very much as if I don't want to tell them my current salary - I suspect I'd do much better if they worked out what they felt I was worth to them and offered me that, rather than taking my current salary and adding a bit extra. The Internet is full of advice that you shouldn't tell a prospective employer your current salary when they ask. But I'm suspicious of this advice - it seems like the sort of thing they would say whether it was true or not. What's your guess - in real life, how offputting is it for an employer if a candidate refuses to disclose that kind of detail when you ask for it as part of your process? How likely are Google to be put off by it?