I think it is a fair question/concern and a noticeable effect with certain combos, especially when you are leveling up and aren't IOed yet.
Yes. IMO some combos can get very very busy but it varies by team composition and the difficulty settings the team runs. The lower the number of support on the team the busier you will get.
From my observations this effect is generally noticeable in pairs with little to no persistent controls (e.g. no pulsing control patches) combined with heal based secondaries. These combos tend to get pretty busy under harder content and/or weaker teams that have no other forms of mitigation.
IMO the best you can do is buff before battle. control and debuff first during combat and heal as opportunities present themselves. In other situations where this isn't enough you'll lean on healing considerably.