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You're asking your question in a very specific way, but it can be generalized to be: "Is it permissible to find ways to avoid fulfilling a *mitzvah*?. If it's forbidden, is it considered nullifying the positive *mitzvah* that was avoided?".

**Rav Asher Weiss** in **Minchas Asher** _Bamidbar_ § 17, found online at his site [here](https://www.torahbase.org/%D7%A4%D7%A8%D7%A9%D7%AA-%D7%91%D7%94%D7%A2%D7%9C%D7%95%D7%AA%D7%9A-%D7%A4%D7%A1%D7%97-%D7%A9%D7%A0%D7%99-%D7%9E%D7%99-%D7%A9%D7%91%D7%93%D7%A8%D7%9A-%D7%A8%D7%97%D7%95%D7%A7%D7%94-%D7%90%D7%9D/), has an article about the inverse question: Does a person have to go out of their way to become obligated in a *mitzvah*.

The article is specifically addressing the idea of the Pesach offering. The Torah says that someone who is too far away from the Temple is exempt, and waits for Pesach Sheni. What if someone is far away, and has time to make it to the Temple if they travel. Are they obligated to do so? First, he writes the following:

> אם יש חיוב להתקרב ואם אינו מתקרב עובר באיסור הרי **בודאי אסור לו להתרחק**
>
> If a person is obligated to travel to the Temple, and by not doing so they're transgressing, it for sure would then be **forbidden to distance oneself**.

So, in this case, he says it's forbidden to make oneself exempt. That is however, if it's a transgression to avoid the *mitzvah*.

He brings a dispute in this. The **Tzelach** _Pesachim_ 3b seems to have no problem if someone doesn't travel to the Temple. Whereas the **Minchas Chinuch** § 5 says a person is definitely obligated to travel to the Temple to obligate oneself.

He then analyzes the **Tzelach**'s opinion. He suggests that the **Tzelach** agrees a person is obligated to make sure they can fulfill a *mitzvah*, and avoid any situation which would make themselves exempt. For example, a person has to build a *sukkah* or purchase the four species, and can't wait until Sukkos comes and say "I don't have, what can I do". With regards to Pesach, since they are already in a state of being exempt (since they're far from the Temple, which the Torah explicitly exempts), they don't have to obligate themselves.

> ואף שחייב אדם להשתדל בצרכי המצוה ולמנוע מצב של אונס ועיכובים מקיום המצוה כיון שהוא חייב בה אינו חייב להכניס עצמו לכלל חיוב אם הוא במצב שבו הוא פטור מן המצוה בדין תורה וזה סברא פשוטה לענ"ד

He then says something which I think more directly addresses your question.

> וע"כ נראה ברור דבאמת אינו מבטל מצות עשה אם לא קירב עצמו לפני החג וכן אינו בכלל מבטל מצות עשה אם לא בנה סוכה או לא קנה לולב וכדומה ובזמן החיוב אין בידו לקיים המצוה, ורק בגוונא שבידו לקיים המצוה בזמן חיובו כגון לישב בסוכת חבירו וכן בד' מינים וכדו' נחשב מבטל מצות עשה, **אלא דמ"מ נענש משום שיש חיוב כללי על האדם לחבב המצות ולהשתדל בקיומן**, וחיוב זה מחייבו לדאוג לפני זמן החיוב שיהיה בידו לקיים המצוה בעידן חיובה, ואם לא עשה כן יש עליו עונש (ובאבנ"ז או"ח סימן שכ"א כתב דמושבע ועומד הוא לקיים המצוות מהר סיני עי"ש), אפילו בציצית שכל עוד אינו לבוש ד' כנפות אין עליו כלל סיבת החיוב מ"מ נענש על שלא השתדל להכנס לסיבת החיוב וק"ו כשהוא מחיוב אלא שלא השתדל להכין צרכי המצוה
>
> Therefore, it's clear that in truth, a person doesn't nullify a positive *mitzvah* if they don't approach the Temple before Pesach. As well, they're not considered having nullified a *mitzvah* if they don't build a *sukkah* or don't purchase the four species, and the like, and when the time of the *mitzvah* comes they're not able to fulfill it. It's only in a case where it's within their ability to fulfill the *mitzvah* during its time of obligation. For example, they could sit in their friend's *sukkah*, similarly with the four species, etc. [If they don't do this], it would be considered nullifying a positive *mitzvah*. **Nevertheless, the person will be punished, since a person has a general obligation do cherish *mitzvos* and to endeavor to fulfill them.** This required attitude obligates them to be concerned before the time of the *mitzvah* arrives, such that they'll be able to fulfill it at its proper time. If they don't do this, they'll be punished (and the Avnei Neizer writes that a person is sworn from Mount Sinai to fulfill *mitzvos*, see there). Even *tzitzis*, that when a person isn't wearing a four-cornered garment they aren't obligated in the *mitzvah*, nevertheless they are punished  for not endeavoring to make themselves obligated in the *mitzvah* [by wearing such a garment]. All the more so when the person is already obligated, they simply didn't make the necessary preparations.

**Bottom line**: If I understood his words correctly, the case you describe would not be considered a nullification of the *mitzvah*. However, there is a punishment for avoiding *mitzvos*, as the person shows they aren't interested in fulfilling them.