About excessive cellular growth
Long story short: Absolutely.

Short story long:

While your intuition that growing a lot of cells can increase the risk of damage that might cause cancer is spot on, your specifics are a little off. It's not the telomeres themselves that are the problem, but broad spectrum DNA damage and transcriptional changes. The condition of the telomeres doesn't directly affect the likelihood of a cell growth becoming more cancer-like. A cell with perfect telomeres fresh from a telomerase-expressing stem cell and cell with shortened telomeres have an equal chance of becoming cancerous. Cell populations with longer telomeres have 'more time' or more chances to develop mutations and cell expression damage, however. You're more likely to get in a car crash if you go to the store across town  than the neighborhood convenience store, even though it's not intrinsically more dangerous per mile driven. 

The sunburn example can be a little misleading. It's not cell regrowth that's the key carcinogenic factor, but instead the direct DNA damage UV radiation can cause. In a particularly bad sunburn your skin cells may be killed or commit suicide(apoptosis) because of the DNA damage they've sustained. If the cells are damaged but do not die, they're likely to recover. Over time and repeated sun exposure, the skin cells that are most resistant to orders from the body to stop growing or die stick around and may grow and divide. Freckles are when this happens to a population of skin cells that ignore orders about how much brown pigment to be, but still listen to the orders that instruct them on how to be skin. When they stop listening to the skin orders, they officially become precancerous.

The acid reflux example is excellent. There are populations of stem cells throughout the adult body that produce skin cells and hair follicles and blood cells and all the other kinds of cells that are more or less expendable. Generally speaking these stem cells don't have do very much work replenishing esophagus cells, so when they are taxed by something killing off the esophagus lining regularly, they can 'break down' and lose control of their own replication. 

It seems like you're both pretty interested in cellular mechanisms of cancer and a little shaky on current theories of cancer formation(there are a few), so if there's a section of this answer that needs to be more detailed or followup questions please let me know.