The gemara[3] lists one who recuperates from illness among the four types of people who must thank HaShem. He does this is by reciting Birkat HaGomel in the presence of ten individuals.
Regarding the extent of the illness, the Shulchan Aruch[4] says that this rule applies to any illness that makes one bedridden, whereas the Rama[5] maintains that it is only for illnesses in which there appears to be danger to one’s life (parallel to the parameters for violating Shabbat for treatment of the ill). Some Ashkenazi poskim accept the former approach, at least when the illness confines one to bed for three days.[6]
One might suggest that your question depends on these two opinions. In order to recite Birkat HaGomel, do you need a true life-threatening situation, or only one which warrants thanking HaShem when He brings a recovery for even a less serious illness? However, many opinions also require some real sickness that causes hardship[7] or might be a sign of something life-threatening to come.[8] If, in spite of the symptoms, the person was not significantly sick and it becomes evident that there was nothing remotely dangerous involved (for example, he receives a negative biopsy result on a suspected malignant growth), HaGomel would clearly not be called for.
This being said, there is strong logic to distinguish between the formal beracha of HaGomel, which must meet certain parameters, and the more general inyan (positive element) of making a seudat hoda’a. The Shulchan Aruch does not mention in this context a requirement to make such a seuda. Yet, we know that such a practice exists, although apparently on a voluntary basis (as opposed to HaGomel). Some cite the following gemara[9] as evidence. Rav Avahu, upon visiting Rav Zeira when he was sick, stated that if the latter would recover, he would make a feast for the rabbis, which he did. Some view this as a source not only of an appropriate thing to do after the recovery, but also as indicating that the promise itself is a segula[10] to help bring about the recovery.[11] If, under these circumstances, one had the impulse to promise such a party, it does not seem right to claim afterwards that the self-obligation was not binding because it was based on misinformation.
Even if one did not make such an obligation prior to his recovery, a seudat hoda’a would still seem appropriate. Even if it turns out that there was no serious illness from which to recover, there still was good (actually, better) news that a perceived problem never materialized. We can illustrate this idea with Talmudic precedent. The gemara[12] relates that Rav Yosef (who was blind) said that he would make a feast for the rabbis if he found out that the opinion that a blind man is exempt from positive mitzvot is incorrect; he wished to be obligated, because one who is obligated in mitzvot receives more reward than one who is not obligated. Here, nothing would change; Rav Yosef was simply hoping for a happy realization, and yet a celebration was appropriate. A similar source relates to the history of the origin of an early-winter pagan holiday called Kalanda. The gemara[13] says that it was instituted appropriately by Adam, who, upon experiencing his first winter, feared that daylight was disappearing due to his sin, until the solstice passed and he saw that the days were getting longer again. Despite Adam’s mistaken impression, as the seasons were in fact part of Creation, the celebration was appropriate (until it turned pagan).
The logic behind such expression of gratitude appears to be as follows. We are always in danger,[14] but it is natural not to feel it constantly. However, when we come face to face with the prospect of our mortality, it is a good time to thank HaShem for our continued existence. Thus, making a seudat hoda’a upon receiving good news that proves that one’s fears were mistaken is a noble thing for one to do, although it is certainly not required.