Nope.
We took students with zero Chinese, and gave them a week's worth of language instruction (TPRS-based, though in the particular setting they were in, they also had a "task-based class", but we did not use vocabulary from that class since it wasn't really acquired by that point). Then we threw a reading at them -- 600 characters long, containing 35 unique characters. We did not show them a Chinese character beforehand, we didn't give them a list, we didn't talk about radicals or character parts or anything. We just put the text in front of them and started reading it with them, and said, "You join in [reading out loud] when you're ready." It took about 3 pages, and everyone was reading out loud together. We faded the teacher voice lead, and they kept reading. We checked comprehension using translation, and they were understanding what they read.
We repeated this reading in various ways (shared reading, choral reading, pair reading, reader's theater) for four days (50 minutes of class per day). Then we gave a test. We thew another Chinese text at the students -- unrelated to the story they'd been reading in class. It contained the same characters, but it had nothing to do with the text they'd been reading. There were no pictures and no context at all with the test (there were illustrations with the class text, and obviously the class had discussed what was going on in the text). Every student was able to read the text and answer comprehension questions in English -- demonstrating that the character recognition skills carried over, despite the total lack of direct instruction in characters.
HOWEVER -- what makes this work is the fact that the students are reading KNOWN LANGUAGE. All the teachers who hear about this want a copy of the "magic text". But the magic isn't in the text. It's really simple -- it's easy to teach someone to read a second language (a person who's already literate in another language, I mean) if they are reading language they already have in their heads. If they are reading stuff they don't really have solidly in their heads, it's a whole different story -- and one that most of us were subjected to during our Chinese study.
As the students become more advanced, they will be able to tolerate more unknowns in the readings, because they will have more structural knowledge of Chinese, and more vocabulary, so that they can make intelligent guesses and use reading strategies to make meaning. But for beginners, we have to keep unknowns to a minimum, or exclude them totally. Not teaching characters separately is certainly a great time-saver, though, not to mention all the materials preparation, correcting, and general wear-and-tear.