Generally correct but in fact FAAAAR more complicated than that.
1) Poor people are not inclined to vote.
And why would they? The "system" as they see it is rigged against them and what good is a vote going to do?
Keeping people poor and creating and fomenting that political apathy is by FAR the best chance Republicans have to grow as a party.
2) When they do vote they don't EXCLUSIVELY vote Democrat though they are outvoted 2 to 1
It's not secret that Republicans frequently speak about threats to social support systems that the poor need to survive. So it's more than a big confusing to see just over 30% of people vote DIRECTLY against their own best interest. Republicans routinely create policies that benefit, first and foremost, those with lots of money. HOWEVER that needs to happen, they make it happen. The more money you have the more you love them.
To be honest though, I'm not going to sit here and crow about how great the Democrats are on this issue; because they are ALSO not great. It seems like Dems governments are beneficial to corporations (as opposed to working class) and Republicans are beneficial to rich individuals.
Wouldn't it be great if America had a political party that had the best interests of the working class at heart? Republicans will argue "rich people will create jobs so we need to empower them to support the the working class (so, essentially "Trickle Down".....it's a special kind of fantasy to think this is actually a thing). Between that and the goal of "lower taxes uber alles", I can understand why some folks may go/fall for that. Democrats are super inconsistent with job making policies but they ARE willing to pass legislation to do things that either keep them safe or enhance their life without them getting greater pay.