The linguists John Lawler and Greg Lee left comments beneath the question indicating that this kind of reduction is plausible:
/'pərsnəli/ is more likely than /''pərsənli/, but @Robusto is right. Any unstressed syllable is centralized (i.,e the vowel usually becomes /ə/) and reduced (usually by simplifying or deleting consonant clusters). Spoken English is nothing like the way it's spelled. – John Lawler May 26 '15 at 19:30
It could happen for some English speakers, but I'm not so sure it actually does. Of your examples, "finely" with 2 syllables sounds best, to me. I don't think "basically" is a good example, because I doubt that it really has 4 syllables (even though its spelling suggests it does). – Greg Lee May 26 '15 at 20:03
There are a great many reductions possible in fluent English speech that are not often written about (actually, I think the same is probably true for any language).
Detailed information about these phonetic processes is often not particularly helpful for English language learners, because in most cases it seems preferable for them to model their pronunciation on careful speech.
The phonetician Jack Windsor Lewis has a web page about this kind of thing: "How English is Really Pronounced". I quoted it in an answer to a somewhat related question, "Is it common to pronounce 'only' as 'own-knee'?"
Here are the parts that I think are relevant to this particular question:
- Many common English pronunciations are either eschewed entirely or given scant treatment by the pronunciation dictionaries EPD (the Roach, Setter et al. English Pronouncing Dictionary), LPD (the John Wells Longman Pronunciation Dictionary) and ODP (the Upton et al. Oxford Dictionary of Pronunciation). This on reflection is not very difficult to understand since it is EFL learners who are the chief recipients of such dictionaries, and such users are on the whole best served by being offered pronunciations that accord most closely with words' ordinary orthographies. The rather sad fact is that recommending the most helpful models for learners and representing faithfully the actual speech of native speakers are to a serious extent mutually antagonistic procedures.
- An example of the many words which have weakforms which cause no stylistic problem is the word only. This is normal-sounding as given in EPD, LPD and ODP as containing an /l/ and it is invariably so pronounced in its prepausal occurrences but, whether stressed or not, on every other occasion it is overwhelmingly most often uttered throughout the whole educated native-English-speaking world without any /l/. There is little gain for the EFL learner to be given this information and the only admission of the existence of this majority form without /l/ is in LPD which quite wrongly categorises it as "non-RP". Another word very frequently to be heard without the /l/ with which it's spelt is certainly which is as often as not pronounced /ˈsɜːtn̩i/ or in a further reduction when not isolated as /ˈsɜːtni/ with not even a syllabic /n/. Another such word is occasionally which is often /əˈkeɪʒni/.
- Longer adverbs ending with -ly are particularly prone to reduction in unselfconscious speech very widely receiving a syllable fewer than is so often indicated in dictionaries. Among examples of this are previously, seriously, immediately and invariably which generally lack any sound corresponding to the internal i of their spelling.
So according to JWL, in some longer words ending in "-nally" such as "occasionally", the ending may even be reduced beyond /nli/ to /ni/. I somewhat doubt that this is common for "personally" (actually, I have found it hard to find audio samples where I can hear "occasionally" pronounced without [l], although I think I have been able to find examples where I can hear the pronunciation of "certainly" without [l] that JWL mentions), but I don't really know for sure, because as a native speaker, my mind filters this kind of thing out. The main point I take from JWL's web page is that there are many common reduced pronunciations in English that aren't common knowledge, but the reason they aren't common knowledge is because it's hard for native speakers to notice them, and it's not very useful for non-native speakers to learn about them. It seems like this kind of information is mainly of interest to phoneticians.