I have two Android phones (ICS and Jelly Bean) and this has not been my experience at all.
The first time you start the Google+ app, it will ask you if you want to enable Instant Upload (which uploads to a private album from which you can publish). Prior to that it doesn't do anything with your photos.
Same for me - but I noticed that it suddenly started syncing to Google+ too a few weeks ago (not sure why it started doing this, either there was an update or it was because I logged into Google+ using the default Android Google+ app and it enabled it then). Either way, I wasn't particularly happy about it, though I believe it uploaded them but did not make them public. I turned it off as soon as I noticed as I don't need my photos synced to two places and I already had photos synced to DropBox.
Both Google/Gmail account and Google Apps account.
I may not be correct about 'any' android phone though. I've only used stock and several custom ROM on Galaxy Nexus ranging from version 4.0.4 to 4.2.2. After you add a Google/gapps account you'll see this in sync setting- http://s24.postimg.org/fxbv98s05/Screenshot_2013_04_28_23_42... . I've found 'Google Photos' always checked by default. First time this feature was introduced, I didn't notice and my G+ filled up with random images from my mobile gallery. Since then I consciously turn this off everytime I flash a ROM.
Edit: so you don't necessarily need Google+ app installed for this to happen.
It isn't true. By default -- including on a brand-new Nexus 4 -- it will notify you that photos are ready to be uploaded, and if you follow-through it gives you the option of automatically uploading from then forward.
Indeed, happened to my very privacy sensitive colleague while setting up his new S3 (he had no prior G+ account, so he got a new one). This may depend on what type of account you have and what terms you have agreed to.
How did you confirm that? Google+ on my Galaxy S III asked me whether I wanted to allow it to upload pictures on first launch (not surprising as it runs the same G+ app as every other device). Of course most people will simply do what nnnnni stated, which is a "sure whatever" clickpast (which Google knows and takes advantage of), and forever more declare it unwanted, mysterious behavior.
1. buy new note2 from att, register google account, skip samsung and att setup.
2. buy new s3 from amazon unlocked, register google account, skip samsung setup.
3. never even open G+ app on both phones
4. take a picture
5. wait an hour
6. you get a notification "pictures you took are ready for sharing" i.e. they are already uploaded against your will and out of your knowledge.
I used the Nexus 4 as an example of the most extensive Google integration. However my other devices are a GS 3, GS 2, Galaxy Glide, and Nexus 7s. Given that Google+ is an app (and is actually the same app on all of them), the same behavior was true on all of them.