Google Ngrams isn't always the answer to things, but in this case it's clear that there's a big British English vs American English split here, and the fell pregnant usage has increased substantially in British English during the past 30 years or so.
As a Canadian English speaker, I'd never heard this at all until recently, and so I don't think a North American English speaker would find it offensive, just odd.
As some of the comments mention, in British English this would not be considered offensive; the Ngram data also seem to support this.
On the other hand, got pregnant is more commonly used in American English compared to British English and is also relatively recent.
Examples of 'fall pregnant' in the British National Corpus
Doing a search for 'fall pregnant' (all forms of the verb) in the British National Corpus reveals that although not very frequent, it does occur, and mainly in speech or reported speech contexts. There are fifteen instances of 'fall pregnant':
1 your Mum to give my money back, she ne--, has your Mum fall pregnant yet? (SP:PS6PT) Nah. (SP:PS532) Tell your Mum to give her money (SP:KP9PSUNK) Er Wayne
2 her life her two eldest children returned home, her daughter because she'd fallen pregnant and her son because his marriage had unfortunately broken down. (video-ends) (SP:PS30A) Very different
3 think I deserved erm (pause) er, two stone. Anyway, er I fell pregnant into the bargain, at the e-- end of the pregnancy weighed fourteen stone and
4 ourselves into a hotel,' she recalls.' It worked. I fell pregnant immediately.' But when I told my father I was ashamed of myself.
5 teenage girls under 16 are having illegal sex. Many regret it and many fall pregnant -- about 170 under 15s in this country every week, according to the Office
6 38, had hoped to keep an affair secret from her husband but she fell pregnant despite having been sterilised. Mr Justice Laws, said in the High Court if
7 boyfriends whom her parents deemed suitable. When she met her current boyfriend and fell pregnant, she had not been able to confide in them. She had been'
8 more mature. At first my mam and dad weren't pleased about me falling pregnant, and they used to go on about how was I going to manage.
9 's plenty have kids on their own round here. In fact the majority fall pregnant and don't get married. " After leaving school at sixteen, she went
10 remanded to Low Newton. While I was there they found out I'd fallen pregnant while I was on my home leave from Bullwood Hall. We were on remand
11 , preferring to see them as innocent children, so consequently when girls do fall pregnant, they have few rights or benefits as mothers. Adolescence is accepted as a
12 for six months or more. It is these teenage girls who more often fall pregnant, rather than those having more casual relationships, as the mothers in this book
13 use it. This gap between learning and behaviour is one through which many fall pregnant. Lots of young couples do not use contraception on their first time, and
14 . Claire and Nickie were both in the process of changing pills when they fell pregnant. Given the information about birth control, whether or not young women go in
15 a jealous boyfriend or husband. There is also the chance of a schoolgirl falling pregnant during vital examinations which can lead to missing out on getting qualifications and eventually jobs
These examples come from a mixture of spoken language (either conversations or reported speech in a written work) and newspaper reports. None appear in academic writing, so this seems like a fairly colloquial use:
Source genres
1 S_conv
2 S_lect_polit_law_edu
3 S_brdcast_discussn
4 W_newsp_tabloid
5 W_newsp_tabloid
6 W_newsp_other_report
7 W_newsp_other_report
8 W_non_ac_soc_science
9 W_non_ac_soc_science
10 W_non_ac_soc_science
11 W_non_ac_soc_science
12 W_non_ac_soc_science
13 W_non_ac_soc_science
14 W_non_ac_soc_science
15 W_essay_school
Best Answer
I would guess that the word "pregnant" focuses on the state of the woman's body whereas a euphemism focuses (or at least pretends to focus) on the anticipation of a child.
Referencing a bodily state or function typically is taboo or disfavored.