Yes, but English is still phonetic. If the speaker slows down it's much easier to understand the person, even (or especially) if they speak in monotone, and even if they don't insert breaks in their speech. Inflection in English primarily serves to assist rapid processing, but especially in business communication it can be dropped entirely. Something similar can be said for word order, and to a significant degree even grammar.

As an American I find it very difficult to under British, Irish, and Australian accents. The inflections really throw me off. But the remedy is easy--ask the speaker to slow down. When they speak slowly, I don't need to rely on inflection. (Except in Cork, Ireland. My Spanish is horrible, but I found it easier to converse with people in Guadalajara, Mexico than in Cork, Ireland. At the bus station in Cork I didn't understand a single word coming out of the clerk's mouth. I know she was speaking English--and not Irish--but beyond that I was clueless.)

Likewise, when I've traveled in Asia and South America, understanding somebody with only basic English skills is relatively easy as long as they speak slowly. As long as I can identify the stream of words, I can reconstruct meaning with high fidelity. English grants huge freedoms in terms of inflection, word order, and grammar. Lurk on any linguistics forum and you quickly learn that it's _really_ difficult to commit a bone fide, uncontestable, error in English. Most of the rules in English are basically regional preferences. I suspect that half of what is taught in ESL classes aren't rules, per se, but merely an attempt at the formalization of the contemporary American English accent (i.e. television speech). The added structure missing from the vague rules of English aids the process of instruction. Much the same can be said for English instruction in primary and secondary school in America.

By contrast, after 15 years of hearing Cantonese on a regular basis I still can't make heads or tails of it. I learned some Korean phrases while on the plane; I still have trouble saying Happy New Year in Cantonese.

It's really difficult for people who have a good ear for tones (whether or not they're musically inclined) to understand what it's like for the rest of us. Many people don't even realize they have a good ear for it, probably because they nonetheless had to work hard at it. But the objective research suggests that if you're a native English speaker who picked up a tonal language, you're not normal, no matter how hard you had to work at it.

One thing I have learned in my cross-cultural experience is that Americans, British, and to some extent Australians heavily abuse sarcasm and cultural references.[1] It's only relatively recently that I've realized how sarcastic I can be (which is less sarcastic than many Americans), and how much confusion and miscommunication it has caused with foreign borne co-workers, friends, and family. And maybe part of the reason Americans rely on sarcasm and cultural references so much is because it's difficult to reliably encode signals in English speech. Emphasizing certain syllables, for instance, often only works regionally. The manner in which a New Yorker draws out a vowel to signal emotional content might actually be the normal mode of articulation in the Deep South. And so almost all Americans, even ones who don't abuse sarcasm, have become adept at recognizing secondary meaning based purely on the word content of speech, not the manner in which it is spoken.

[1] I suspect Germany and maybe even France might be similar in that regard. I doubt the phenomenon is unique to Anglophone countries; it's probably partly a function of modern Western culture. But the nature of English probably plays a part, too. Anyone care to confirm or contest?