Despite the United States being called "A Melting Pot" it's not uncommon for immigrant communities to form clusters in regions for a number of reasons. Armenians first started to come to the U.S. to escape the Ottoman Empire's persecution of Christian Minorities, and on advice of American Missionaries in the regions, who were sympathetic to the plight of the Armenians. While the first settlers came to the United States via Atlantic Transit mostly because of the more reliable port infrastructure and industry and European ports with ships bound for the U.S. were closer enough for Armenians to travel too. However, with the 1850 admittance of California to the union, combined with favorable attitudes towards Armenians from the Russian Empire, it meant that while it might be a longer journey to Russia's Pacific coast, it was far safer than going to a European power as Armenians would avoid a journey through the Ottoman Empire. By 1870, the city of Fresno already had a large population of Armenians (at the time, most Armenians coming to America were farmers and Fresno's primary industry was farming), which meant that when the first large wave of Armenians came in the 1890s, the city of Fresno had some semblance of familiarity (This isn't an Arminian only immigration trope either. Most major ports of entry in the United States have large ethnic neighborhoods or districts because immigrants from certain places tended to rely on support of immigrants from their home country, especially with the language and cultural barriers in place. The Armenian community is likened to the strength of the German American community in it's organization (The German American at this time was quite strong and very active back in the early 20th century. However, world events would soon make German Americans less willing to bring up their German heritage despite the fact that German Americans are the largest ethnic minority in the United States.).
That all said, the Armenian dispora in the United States is still to this day, largely clustered to a few locations in the United States, which in turn concentrates their votes (hence why many politicians of Armenian descent are elected in California.). The Armenian American Lobby is quite influential and is said to be on par with major lobbies like the oil industry lobby, but in terms of advocacy, the lobby focuses more on lobbying for policies favorable to Armenia as well as recognition of the Armenian Genocide (which is easier said than done by U.S. Foreign policy, as doing so would damage U.S.-Turkey relations... and considering Turkey is a NATO ally and allows the U.S. to set up short ranged nukes targeting the U.S.S.R, pissing off Turkey is not something the State Department would like to deal with.).
The reason that Nancy Pelosi would give a speech in Armenia is 2 fold. First, as Speaker of the House, she is one of the major leaders of the United States and in charge of running the legislature, which means she has huge policy making power, especially when you consider that any law that allocates federal spending must originate from her half of Congress, and to say nothing of the fact that she is second only to the Vice President in the presidential line of succession. In addition, Nancy Pelosi is a California representative, specifically San Francisco, which does have a sizable Armenian population, so a speech to Armenia would be smart for her prospects for re-election. While she does not need to worry about losing her 2022 election, other California democrats are and this might help them with Armenian voters in their districts.
All that said, the Armenian vote is not likely to impact the 2022 midterms in a noticeable way, since the population isn't spread out. At best it would affect the California delegation to congress which is the largest in the nation with 52 reps and 2 Senators. But the balance of power will likely not shift with the Armenian Lobby and it's agenda. Even if the House flips, the most likely new Speaker of the House is Kevin McCarthy, a Republican from California.
