might indeed imply something. At the most general level, and weakest claim, that one has to appreciate the bounds set due to the extreme degree of holiness, and the manifestation of Hashem, such that care must be taken.
On the other hand, this looming possibility of death in overstepping bounds in kodesh is not restricted to Aharon. If we look to the previous perek, we have:
But back to the first hand, note the repetition, spelling out the incident: "when they drew near before the LORD, and died." This might be cast as simple reminder, but it might be cast in a different direction as well.
One can say further, along the lines of this juxtaposition. The precise nature of Nadav and Avihu's sin is not clear. And midrash, and even peshat, may be to determine the nature of their crimes from this juxtaposition. Perhaps Nadav and Avihu trespassed in this exact way, and that is why Aharon is now being warned about it.
Now on to the meforshim and their positions. Rashi writes:
Thus, what happened to Aharon's sons serves as a memorable warning, and so including this reference in the pasuk, dating it, is somehow akin to mentioning it. And Rashi works in the comparison there. Is the actual they did precisely this actions. One could read Rashi that way, I think.
Ibn Ezra writes:
Thus, he maintains that this is precisely their sin.
There are elements of merely fixing the time, but also connecting the cause, of not going at all times into the kodesh.
Seforno just has it as going past what one is commanded. Thus:
Rashbam also connects the cause, of not entering the mikdash when not in accordance with law:
וְ"אַחֲרֵי מות שְׁנֵי בְּנֵי אַהֲרן" אָמַר לְמשֶׁה "דַּבֵּר אֶל אַהֲרן.. וְאַל יָבא" שֶׁלּא יִכָּנֵס יותֵר מִמַּה שֶׁצֻּוָּה "וְלא יָמוּת", כְּדֶרֶךְ שֶׁמֵּתוּ בָּנָיו בִּהְיותָם הורְסִים לַעֲשׂות קְטרֶת יותֵר מִמַּה שֶׁצֻּוּוּ. וְזֶה 'לְזַרְזו יותֵר מִן הָרִאשׁון'.
Aharon ben Yosef the Karaite takes issue with Ibn Ezra. It is entirely to fix the time, just as in the examples Ramban gives. It is to show that it was immediately after their death. But it is not showing their sin. For Aharon their father did not enter there, so how did they enter? And further, one can say according to his words that they were drunk, for the warning was after this immediately. (This is the position of Rabbi Yishmael, brought down by Rashi as the details of their sin.)
I don't know. Semichut overdone is drash, but some semichut is what we call context; and it pays to pay heed to nuances in the text. However, at the most, I would say that the purpose is to show the danger involved, and the awe one must have, in dealing with kodesh.
א אחרי מות : אעפ " י שהם לא נכנסו לקודש הקדשים , מכל מקום היתה מיתתם מפני זילזולם בכבוד ובמורא הראוי למשכן ה ' ולעבודתו .