Well, exact achievable radio transmission distances can only be determined by on-site measurements (and are still highly variable due to weather). However, I'll try not to make this any more vague than necessary.
The unit you linked has a max. transmit power of +12dbm (about 18mw). For comparison, the most powerful wifi router I just found on a Google search has ~28dbm (800mw). While 800mw may at first seem hugely higher than your 18mw, radio signals decrease exponentially with range, so the dB ratings can be used as a (comparative) straight-line "measuring tape;" meaning that the ~28dBm router would only have about 2.25x the range of your 12dBm chip.
Now, while transmit power may have a relatively tiny effect on usable distance, antennas come in a WIDE difference of relative "powers." Most "normal," router-mounted wifi antennas achieve between 3-5dBi gain. Meanwhile, some of the better commercial antennas (like this one) can achieve 24dBi or better, which means a good (24dBi) antenna on a weak (12dBm) transmitter can "out-reach" a high-power (28dBm) transmitter with a decent (5dBi) antenna by a factor of 36/33.
So, for a short answer, if your cell phone can get a wifi signal from where you want to use your device; there should be no problem just slapping any wifi antenna on that chip. BUT if the cell phone's out of its range, you can add up to ~8x more range to that chip by attaching a high-gain antenna; then nearly double the range again if you install another high-gain antenna on your router (high gain antennas are directionally sensitive, and only work well if pointed straight towards the other transmitter/receiver).