Conventional wisdom would dictate that, yes, using heavier strings on an electric guitar will result in fatter tone. More metal vibrating in a pickup’s magnetic field should result in more output and bigger sound. And in practice, this often holds true — Stevie Ray Vaughan is the classic example of a guitarist who used heavy strings and certainly achieved a big tone!
Having said that, it is undeniably possible to achieve big tone with very light strings. Here, the classic example is Billy Gibbons of ZZ Top. Billy is known for using the thinnest gauge strings he can find, yet his sound is thick and rich. Brian May uses thin strings. Jimmy Page famously suggested that new guitar players use lighter strings.
As with most things, in either direction there are trade offs. Heavy strings can be harder to play. Ultra-thin strings can make it difficult to maintain intonation and require a light touch. So your technique may need to be adjusted — which can also affect your tone.
And there are additional contributing factors: action height plays a role, as do the pickups on your guitar and how close they are to the strings, the amp you use, the type of sound you’re going after, the amount of gain you use, any effects in the signal path, and more.
Fortunately, experimenting with different string gauges and their effects on your tone is not an expensive proposition. Why not purchase sets in various gauges, put them on your guitar, and record each one through your amp? (Make sure to keep the amp at the same settings and the microphone in the same position for each recording.) Listen backand see if you can hear a difference in tone. (This works even better if you can arrange a “blind” listening test, where someone else switches among the recordings of the various string gauges.) Then weigh that difference against any technique compromises you might have to make in order to play those strings.