There's no guarantee of consistency from episode to episode, but Homer probably doesn't run up much of a tab because Moe wouldn't stand for it. (The Barney joke aside, Moe cares about money too much to let his "friends" run up large tabs).
Trash of the Titans
Moe: Woah, woah, hey, you didn't pay for the beer Homer: Can't
someone else do it?!
Moe/Homer: hahahahahahahahaa (Homer exits, you
hear a gun)
Moe: Seriously, gimmie the money!
In the episode Duffless
Marge: Mmmm. You don't have to start drinking right away. I was
thinking we could go for a bike ride.
Homer: But Marge, the barflies are expecting me. Larry, and Barney,
and that guy who calls me Bill.
Marge: But you look better, you don't sweat when you eat any more, and
look -- [holds up a wad of cash] you've saved more than a
hundred dollars. I found it in your pants.
Homer: [snatches money] Yoink!
Also in that episode
Barney: But Moe, yesterday you called Homer a worthless sack of --
Moe: [strikes Barney] Pipe down, rub-a-dub!
And in Burns_Verkaufen_der_Kraftwerk, Homer flaunts the "Cool" $25 he made off his stock options and buys a duff private reserve.
While consistency isn't a requirement in Simpsons' writing, I think it's safe to say that Moe doesn't extend Homer much of a tab and he'd probably throw him out the day Homer runs out of money (though I don't remember Moe's coming up in any of the Homer is broke/unemployed episodes). Moe kicking out the designated drivers and calling them deadbeats in one episode and him asking himself "what am I going to sell to Barney now, and buying an espresso machine to sell Barney coffee when Barney stopped drinking).
I think it's safe to say that Moe doesn't make much money cause Moe's is never full (exceptions being the flaming Moe's episode and the family feedbag episode and I'm remembering one other when he made the place all hip and trendy and his artistic consultant had Homer sit in a dark corner by unscrewing the light).
I think it's much more consistent to say that Moe insists on being paid and rarely to never allows his customers to run a tab into the following day. The bit about sending Barney's bill to NASA was the inconsistency.