Yes, if you have enough of it and you actually export it. Most people don't have nearly enough and then they keep it in the tank and it starts to die when it gets depleted of some nutrient (like iron)... so it is oftentimes just a temporary store, or not enough. There are people with like 240-300 gallon tanks that use kiddie swimming pools to grow enough chaeto to keep P down.
The other issue is that the DSB&Pl will outcompete the macro for N, so it won't grow as fast to use up the P. DSB&Pl are rock solid to get N to zero... chaeto and macro is just one of many things to help with P, IMO and always works better in academia than in practice unless you have a TON of it and sometimes even dose some sodium nitrate and iron. A bad-azz skimmer, or two skimmers, is going to do way more, IMO.
Read up on Iron dosing for macroalgae... it will need it if you have any significant amount.
My typical tank has a DSB and lots of pacific live rock (porous and P free from the ocean). After 2-3 years, I put in new sand in about 20% of the tank every 3 to 6 months. ...then repeat. This gets the phosphate clogged sand out and allows more to bind to the clean sand.
BTW - I still know quite a few people who will set up new tanks with Plenum. They don't need anything and don't hang out online and argue about the newfangled methods, but you can bet that their tanks are awesome and have been for years and will be for years. Most all of my old-school friends replace sand and some even have extra live rock that the rotate in/out of the tank after cooking it to rid of the phosphate that binds there too. If I did not have coral all over my rocks, I would rotate them too.