Marching is the first necessary step to get people organized. It is the lowest bar for starting to organize and to participate. It is where people can drum up support, awareness and donations.
I listened to an hour-long podcast in which Chris Hayes interviewed Alicia Garza, who co-founded Black Lives Matter (BLM). They talked specifically about this question and since you're interested, perhaps it would be one place to go to hear informed organizers/activists discussing it. It aired on June 4.
Besides BLM, one other recent place in which this question of "are demonstrations enough" comes up is, of course, Occupy. (In that case: no, demonstrations were not enough.)
One thing I remember Garza saying is that the ability to organize a large, nationwide march on Washington showcases the scope and depth (down to the grassroots level) of a movement. If your movement isn't broad and organized, your nationwide march will not succeed.
But that's a necessary condition for political action, not a sufficient condition. A movement can't let marches be the endpoint, and in the interview, Garza emphasized this.
Clearly the organizers of the 1993 "March on Washington for Lesbian, Gay and Bi Equal Rights and Liberation" (which I attended) did not view the march as an endpoint. Many of the roughly 600K (+/- 300K) people present had a lot at stake, including their jobs, at that time. The march was more of a focal point, a coming of age. A constituency made visible. But not an endpoint.
Of the set, ACT UP was arguably the most successful, and probably deserves much of the credit for mainstreaming gay / nonbinary gender culture.
The WTO protests are more mixed, but put a damper on the Washington Concensus / Neoconservative Agenda movement. Global trade meetings are no longer casually-hosted affairs, and now tend to be in remote / secluded locations.
The Iraq War protests were arguably the least effective, though massive in many cities. They simply disappeared off news coverage though. Clearly they didn't stop the war or lessen the catastrophic impacts of it, though they did help cement a strong political divide over it in the US.
Whether or not more recent movements, particularly on the right, could be considered mass / popular uprisings is a fair question. I'd be inclined to say "no", but a case might be made for the Tea Party and alt-right movements.
I'll be the first one to sound the 'correlation is not causation' alarm over and over. After all, maybe the social issue is getting enough people to protest because society is already on the verge of change, rather than society changing because of the protests. Protesters may be getting the causation backwards. However, there's some evidence that protests are helpful in causing change.
My favorite study to establish a directional causal link looks at policies enacted after protests, accounting for the effect weather has on protests. The weather is presumably random enough to not be related to where society is, and it affects protest turnout, which lets you connect protest turnout to policy change causally. It's not definitive, but yeah, there's decent evidence.
I disagree with the other poster who is suggesting that marching is a necessary step for change, but it does seem to be a useful instrument for it.
Yep it is a solid way to meet people who might also have an inside track to influencing the institutions of a given government. It also gets eyes on your cause when it's not right in the front of society at large. A lot of it is just to get otherwise ignorant people becoming aware and seeing the activists are just people like them trying to make a fair go of it.
Perhaps it's necessary but not sufficient: if you have zero lawyers, press, or government officials on your side, marching is a great way to get thrown in jail for "rioting" and have your reputation destroyed.