No, this wouldn't work.
When you're under the effect of the tongues spell, "any creature that knows at least one language and can hear [you] understands what [you say]."
The "speak friend and enter" example you are referring to would not work for the following reasons:
The effect of the spell only causes creatures to understand you, not objects or effects, so the door in question would not be able to react to the trigger word as you've spoken it in a different language unless the word is the same in both languages. (If the something in question is instead a creature, refer to the following point, which still applies anyway.)
The effect changes how you are understood but does not actually allow you to speak another language, so you are incapable of speaking (literally uttering the sound of) the trigger word as it ought to sound unless you happen to know how to speak it properly in the original language. (This is based on my understanding of the example door, which required clever wordplay in a specific language. It might be contentious in some cases whether the sound or the meaning of the word triggers the reaction, but I've stuck with the example in question, because addressing all possible word-based triggering mechanisms is beyond the scope of this question.)
Of course, if it's interesting or clever, a DM is within their rights to allow this scenario to work.