Question: I have heard that a chatan during the week of sheva berachot does not need to daven with a minyan. Is there anything to that, and what would the reason be?
Answer: There is something to what you have heard, but it has less to do with a minyan than with going to shul. Let us discuss the issues and put things in perspective.
The Shulchan Aruch (Orach Chayim 131:1) says that Tachanun is not recited in a chatan’s house because the simcha of a chatan and the somberness of Tachanun do not go together well. The Rama (ad loc.) says that this is even when the chatan comes to shul, but only on the wedding day. The Taz (ad loc. 10) says that it applies all seven days after the wedding and comments that for this reason, a chatan should not come to shul during this time so as not to deprive people of Tachanun. The Mishna Berura (131:26) cites the Taz without dissent.
Contemporary poskim point out that some disagree with this restriction/recommendation (see Nitei Gavriel, Nisuin 63:4; Dirshu 131:(41)). Let us briefly analyze. While the tzibbur rarely minds missing Tachanun, it is an important prayer (see Mishna Berura 131:1). Still, should we exclude such an honored person (see below) who has done nothing wrong? Rav S.Z. Auerbach (cited in Tefilla K’hilchata 15:(41)) posits that according to the Rama, that it is only on the wedding day, people are correctly happy to share his simcha at the price of Tachanun, but for the Taz, who applies the exemption for a week, it is more of a problem to take away Tachanun that much (we hope for many weddings during the year). In answering why a mohel is not told not to come to shul, he also adds that due to the stature of a chatan and his (one-time, iy"H) 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. I would put it this way. Consistently davening in shul helps the individual and Klal Yisrael. A chatan personally has a halachically recognized competing reason to stay home (like the halacha to not go to work that week). The fact that his presence deprives the community of Tachanun is enough to tip the scale in favor of davening at home in the presence of his kalla.
Another reason not to go to shul is the concept that a chatan (and kalla) should not go on the streets by himself (Rama, Even Haezer 64:1). Some explain the practice based on concern for his physical and/or spiritual welfare (based on Berachot 54b). Others (Perisha, Even Haezer 64:1*) connect it to his stature resembling a king, who does not go unaccompanied (Pirkei D’Rabbi Eliezer 16). There are questions as to whether this applies in safe places/times (daytime). In any case, an escort of one including the new spouse suffices (see Nitei Gavriel, Nisuim 56:(10)), so this impediment is solvable.