Practical Answer
"it depends" on how your hold your phone, the layout of the space you're in, how many walls, what's in the walls, etc.
Unfortunately, the real-life answer is to just boost the AP power and see if you can connect, and if you can connect some speed-test data to quantify how well you're connected.
For example, you may get a useful connection 100m in one direction that has no obstructions line-of-sight, but only 20 meters in another direction because there's a couple of walls between you and the AP.
Your intuition is correct: just because your phone can "see" an AP doesn't mean it has the juice to connect to it.
Nerd Alert
The theoretical answer depends on at least the following variables:
- EIRP transmit power of your phone
- Radiation/Reception pattern of the AP antenna (assuming it's not isotropic)
- where your phone is in the pattern.
- the sensitivity of the AP's receiving stages
- the signal:noise ratio at a given location
- more stuff too :-)
1Unfortunately, a laptop has typically a very different WiFi antenna than a phone, and, is typically differently positiond. (not enclosed by a palm). I typically can connect much better using a laptop than with a phone. – Marcel – 2014-09-11T14:36:16.257