How long will this strategy work? (TZ 2v2 marauder+cs/speedling push against PP, TP shared base)

My 2v2 partner and I are Terran/Zerg and in high bronze, working on our fundamentals to get into silver/gold. When playing a walled off (shared base) Protoss and Protoss or Protoss and Terran we've started developing a push of 5-10 marauders with concussive shells and 20 or so speedlings. We go into push mode if we scout and they are not rushing.

We rally close to the enemy base, and then I head in first with marauders focusing my firepower on the weakest point in the wall. Once the wall is busted, he rushes in with his zerglings and tries to do economic damage. It's a little like a baneling bust. In bronze this has started to work really well. If we don't roll over them, we usually do enough damage that successive waves of attacks eventually win the game.

I haven't seen the marauder/ling as a recommended team combo. Should we be continuing to work on this build? Will this be effective in silver? What counters should we look out for?

You should generally try to learn a variety of builds. While what you're doing is smart, it's also pretty easy to counter if scouted and as you go higher in the ranks you'll run into better scouting. You don't want to rely on one build for all of your wins because then when you stop doing that build you'll be completely outclassed.

Marines will beat your Marauders cost for cost easily, and any units produced defensively will give the defender an economic advantage. Just sitting with Zealots and Stalkers/Marines at the top of a choke point puts your army in a tough spot.

Your build is great against double Protoss, though. Protoss earlygame generally relies heavily on Forcefield in 1v1 games, but the ramps are bigger in 2v2 maps so it doesn't work quite as well. If you can micro your Marauders well they completely crush Zealots, and after you bust the wall the Zergling flood is too much for Stalkers.

A build like this could work as a timing attack even in Diamond/Masters against opponents trying to fast expand, but that's not a very common option in team games. I'd suggest working on a more economic build, such as a 2 Barracks FE. Your partner can go for a Speedling Expand or Hatch First. Learning to play more macro-economic games will be harder at first as you struggle to defend all-ins, but it's a far stronger way to play.