Time needed to clear customs and immigration at Frankfurt airport?

11 to 1 pm is only 2 hours by my calculations! What if your plane is late? Furthermore, even arriving at 11 doesn't mean that you are out of the plane at 11 -- all those people getting their luggage out and shuffling off the plane have to be taken into consideration. Do you have luggage to pick up as well?

What kind of passport do you have? Do you have a visa for Schengen? This will probably take longer than if you have an EU passport.

You might make it, but you might not. Is that ticket changeable or refundable?

#1 raised the questions that are relevant to make a guess. Furthermore: Which airline (terminal 1 or 2) from which city (Schengen or not). Familiar with Frankfurt airport or not?
And what exactly is your concern? Are you going to make a reservation only, i.e. reserve a specific seat on a specific train, but holding a flexible ticket? If yes, don't care too much, take the next train, which may include a train change in Cologne. If it is not holiday season, trains are usually not crowded around midday or early afternoon, so no urgent necessity to secure a seat in advance.
If you are considering to buy a special fare ticket which is restricted to this specific 1 pm train... well... it's likely that you will make it. But a slight delay or a longer line at immigration will make you to rush, and if some problems accumulate, you may miss the train. If this happens, nobody will refund you a non-flexible ticket. Keep this in mind when buying the ticket.

(Quote): I will be landing in Frankfurt at 11:00 AM

That's if your flight is on time, many aren't. I'd say yes, possibly, but also no, possibly.