I use 275 gallon totes myself. It takes almost no rainfall to exceed the capacity of a 1" vertical pipe to move water - air has to escape as well.
Forget "should suffice" - the experience of plumbers since at least the Roman times says otherwise. Don't get me wrong, I love theory, but at the end of the day, reality always trumps it.
There's a reason why your house is almost certainly plumbed with a 3" dia vertical air stack, even though the supply line for the home is probably only 3/4" (admittedly, pressurized).
Placing an angled 1" pipe at the start only serves to reduce inlet area further, hopefully allowing air to escape, but also ensuring you likely can't capture much rainfall. 1" dia pipe has an inlet area of about 3/4 sq inch.
In KC, MO, a 5 minute rainfall rate of .4" is an annual event at 90% confidence, a rate of almost .7" in that period is a 10 year event.
SOURCE If your shed or coop has a mostly flat roof (so we can discount velocity) and a surface area of, say, 64 sq ft (8x8), that's 9,216 sq inches.
9,216 square inches x .4" of rainfall/5 min is 3,686 cubic inches/5 min, or almost 16 gallons of water in a 5 minute period. Under those conditions, a 1" diameter pipe needs to move water at a rate of 3gpm while allowing air to escape at the same rate. That's more water than comes through a showerhead under pressure (if manufactured for US use after 1992). Its about 5.5 gallons a minute for the 10 year rainfall rate.
Plumb it with a 2" line, you can move 6x more rainfall, and likely never have a problem. Its also much easier to clean out.