Do I have time to visit downtown London during a 4-hour layover at Heathrow?

4 hours from Heathrow really isn't going to give you sufficient time:

• Immigration. Their official service standard for non-EU citizens is 95% of passengers getting through in 45 minutes or less. They don't achieve that standard. It's hard to predict, as you don't know how many flights are arriving at the same time as yours, but this could take an hour or more.
• To/from London. By Heathrow Express, which is fast but expensive, it's a 15 minute trip and runs every 15 minutes. So that's a half hour of train time, plus 0 (best case) - 15 (average case) - 30 (worst case) minutes of waiting time, plus time walking to/from platforms.
• Back to Heathrow. It's a large unfamiliar airport, and you'll need to go through security and get to your gate sufficiently before boarding closes, or you'll miss your flight. Let's say you aim to get back 1.5 hours before your departure time.

You'd be left with 30-45 minutes of actual free time, and you'd be starting at Paddington Station, which doesn't give you much for an iconic photo.

And any complication (a delayed flight, a longer wait at immigration or security, a small train delay, etc...) would be enough to mess this up.

I personally enjoy madcap adventures doing layovers, and I'd skip this one. You could buy access to a lounge in your terminal if you want a more comfortable place to wait.