Yes, but if you have a good GPS reception with no window/roof in-between you get a 5m radius, while otherwise having a 15-20 m one.
I found speed to be another important factor to consider. Because the position is updated once per second, if you go faster than 35 km/h, your position will be updated less than every 10 meters. Then biking is fine.
Most devices I tried aren't that good when it comes to tracking on foot.

A direct satellite facing GPS device is also less prone to lose signal, and it will "see" more satellites.
3 satellites in view is necessary to get a 3D fix.
Because you can lose signal or have a weak one, the more satellites in view you have, the better the accuracy of the mapping.

There is no point to create a path on JOSM following the exact position of each logged GPS point. The goal is to get an idea of the shape of the road. It wouldn't make sense neither because GPS is not accurate enough. If the GPS track shows something like /\/\/\/\ (with less angles) the road was probably straight.

I'd like to see a weather-sealed Bluetooth GPS mouse/data logger with long battery life that would provide a better solution compared to smartphones internal GPS.

Thanks for your comments.

Well, considering the $650 price tag of an iPhone 4...
If you are only looking for a GPS logging capable smart phone, $150 is fine.
I paid $350 for a 1 month used Galaxy S, and I find it very cheap for what it is honestly.

A Garmin eTrex for example is $250, so...

Thank you for the good advice, but I can't afford it.
I'm actually an high school student, and saving money to pay my driver's license.