There is something to what you have heard, but it has more to do with reasons not to go to shul than with the chatan not needing a minyan. Let us discuss the issues and put things in perspective.
The Shulchan Aruch[1] rules that Tachanun is not recited in a chatan’s house, because of the incongruity of the simcha of the chatan and the heart-wrenching supplication of Tachanun.[2] The Shulchan Aruch and Rama[3] write that we refrain from Tachanun not only in the chatan’s house, but even when the chatan comes to shul, but only on the wedding day itself.[4] The Taz[5] extends this halacha to include not only the wedding, but the six days that follow as well, and he comments that as a result, a chatan should not come to shul during this time, so as not to deprive others of Tachanun. The Mishna Berura[6] cites both of the Taz’s ideas without citing dissent.
Contemporary poskim point out that some disagree with the recommendation for the chatan to avoid coming to shul.[7] While the tzibbur rarely minds missing Tachanun,[8] it is a powerful prayer, especially when coupled with nefilat apayim.[9] On the other hand, is it right to exclude such an honored person as a chatan, at such a joyous and critical time in his life, from joining a minyan? Rav S.Z. Auerbach[10] posits that according to the Rama, who maintains that the Tachanun exclusion is only on the wedding day, people are appropriately happy to share the chatan’s simcha at the price of Tachanun. In contrast, according to the Taz and our minhag that the exemption is for an entire week, it is more objectionable to be deprived of Tachanun so often (as we hope for many weddings during the year).
Why is a chatan different from a mohel, who is not told to avoid shul, even though Tachanun is similarly not recited in the presence of a mohel performing a milah that day? Rav Auerbach explains that due to the halachic status of a chatan and his preoccupation with his new wife and status, the importance of his tefilla b’tzibbur is diminished. This explains why we may prefer him to not come to shul. We might put it this way: Consistently davening in shul helps the individual and Klal Yisrael. However, a chatan personally has a halachically recognized contrary indication. Considering that the chatan maximizing his time at home with his newlywed wife is important enough during this week to make it forbidden for him to work,[11] and considering that this period includes exemptions from certain mitzvot at certain times,[12] there is a practical silver lining to his not having to go shul. The fact that his presence deprives the community of Tachanun is enough to tip the scale in favor of his davening at home in the proximity of his kalla.
Another reason for the chatan not to go to shul is the concept that a chatan (and kalla) should not go on the streets by himself (or herself).[13] Some connect this rule to the chatan’s stature, in that he resembles a king, who does not go out unaccompanied.[14] Others[15] explain the practice based on concern for his physical and/or spiritual welfare.[16] There are discussions as to whether this applies in safe places/times (daytime). In any case, an escort of one, including the new spouse, suffices,[17] so this impediment is solvable.
We now turn to practical guidelines and perspectives. If there is a minyan at a sheva berachot, the chatan should take part, and this should also hopefully make the kalla happy. Going to shul can depend on the circumstances. If the couple is careful about not going out alone (which Askenazim, especially those with Chassidish leanings, are more likely to be), then the chatan should consider the feasibility of the alternatives. Does he have someone to escort him both ways, without unreasonable inconvenience for the escort or disappointment to the kalla? Is it feasible for the kalla to come to shul herself, and is she interested in doing so? How important is it to the chatan to not miss minyan, even during such a week? How important is it for the kalla that her chatan does not miss minyan “because of her” and that he/they thank HaShem for their marriage and add requests for their future success at an optimal setting (shul)?
It is not always simple for a chatan to raise these questions and get honest answers from his kalla about what she really feels. Therefore, some rabbis might wisely say that the default position is that the chatan should not expect to go to shul. However, if based on personalities and circumstances the couple deems it desirable, there is insufficient reason to preclude the chatan from going to shul.