I've used TC for both my DSs (deaf, additional language disorders) in a sign-supported English mode, reinforced with other visual stimuli / clues. We used BSL signs rather than Makaton, following spoken English grammar and syntax.
I'd definitely recommend it for early years, but our circumstances might not map directly onto yours. We went down the TC route because the DSs have variable, progressive hearing losses, and it took a very long time before they could get good access to sound.
There are definite pros to this approach - when the auditory processing load became too much for them, the signs often made the difference between them getting the gist of a short sentence and understanding it completely. It helped massively in noisy / outdoor situations where they couldn't hear well. The DSs didn't have any obvious sensory overload problem in listening and watching for signs simultaneously. And for us, it provided an entry into basic BSL, and building blocks for them to enter deaf culture.
Downsides - Hard to keep going in mainstream education - the DSs went to a mainstream / unit combo where its use was well embedded across the curriculum. Learning the signs isn't necessarily easy at first, particularly once you get beyond the basic iconic stuff. It's also really fucking tiring to communicate in two modes simultaneously - both for me, and for them.
We've moved to a more-or-less purely oral mode of communicating now - basically, their language moved on to a point where the TC approach was getting in the way. I simply couldn't sign and speak and communicate in sentences with multiple elements of information all at the same time. I could do two of these three simultaneously, but not three. At that point, we junked it...