For practic purpose, producing the proper aspiration of English voiceless consonants by Russian learners is more important than the ability to pronounce "partially voiced" consonants, which are unusual for Russians as well. If you say "ben" with the fully voiced Russian "б", it will still sound as "ben", although the accent can be noticed. But if you say "pen" with the Russian tenuis "п", it can be taken for "ben".

Similarly, for practic purpose, producing the proper full vocing of Russian voiced consonants by English-speaking learners is more important than the ability to pronounce "tenuis" unaspirated voiceless consonants. If you say "пар" with the aspirated English "p", Russians will still take it for "пар", although the accent will be noticeable. But if you say "бар" with the English partially voiced "b", it can be taken for "пар".

There are some links where this issue is discussed in details:

phonetics - What is the difference between voiced and voiceless stop consonants? - Linguistics Beta - Stack Exchange

quotations:

"As a native speaker of American English, when I was listening to the difference sounds in this IPA chart, I was really surprised when I realized that I could not differentiate between p/b, t/d, and k/g. (I think I've always been distinguishing the pairs based on whether or not the consonant is aspirated.). I know the difference has to do with vibrations of the vocal chords, but I am not quite sure what to listen for."

"So what does this mean for you. As a native English speaker, you have only ever been exposed to [p] aspirated and [p] unaspirated. You understand the former to be /p/ and the latter to be /b/.
When you get presented with a sound you've never heard before in that particular phonetic environment, your brain just associates it to the nearest match. Your brain disregards the voicing before the stop release and notices that there is no aspiration duration, concluding immediately that it is also /b/. This is helped in large part in that in even slightly rapid speech, the English sound /b/ appears not as an unaspirated [p] but actually a fully voiced [b] (e.g., in the word tabs).
And that's why you may not be able to tell."

http://answers.yahoo.com/question/in...4071028AATF9L4

quotation:

"I can clearly distinguish (b, d, g) from (p, t, k) spoken by native US/UK English speakers. People can clearly distinguish my (b, d, g) from (p, t, k) too. To me, the only perceivable difference between the two groups is that a puff of air comes out when we say (p, t, k).

However, when I listen to Japanese, Spanish or south Asian speakers, sometimes I cannot distinguish the two groups. To me, both of them sounds like (b, d, g). However, apparently other listeners (including native US/UK speakers) can still distinguish them."

zompist bboard • View topic - Voiced/unvoiced plosive distinction in English

quotations:

"I've read more than once that the distinction between voiced and unvoiced plosives in English is more a distinction between aspirated and non-aspirated, and to a native speaker's ear a non-aspirated initial plosive (in a foreign language) sounds voiced (and also that non-aspirated and hence voiced initial plosives carry very little voice)."

"I remember an article in the New York Times about a fairly recent paper that showed something similar happens if the audial and tactile information are out of sync: e.g., one tends to hear /ta/ for /da/ (are slashes appropriate there?) if a air is blown onto one's hand. I assume the test subjects were native English speakers, but the article didn't specify."The latter is probably a typo, logically it should read "[da] for [ta]", I guess.