I'm betting that this is 90% likely to be a bad idea in the long run. One could not be certain, though, until one knew the entire path of drainage, including the elevations. You'd need to spell out every detail. Pictures, that include surroundings, always help.

In the vast majority of instances, people are not going to use the patio during the rain. So using the patio as the splash block, directing water onward, is usually no problem at all. Whereas, many times, buried drainage becomes a problem. (It depends a lot on how it's configured.)

not the best picture, but an idea... the yellow outline will be the new pad (rip out old pad and repour) and you can see the current gutter. I will run it from the house wall out to the right where there is a natural drain area in the yard. It will run about 14' under the concrete then run an additional 25 feet in the yard to daylight. I plan to use PVC pipe under the pad then use dual wall corrugated for the longer run.

What if you went the shorter distance ?

The short distance will drain into my driveway... here is a Ariel view of the patio... the yellow line shows the ~40' drainage run... i need to get it out beyond the white thing as there is a retaining wall (in red) with concrete for that RV there... the blue line shows the natural "ditch" that water runs down and runs into the road drainage ditch.

For me it's all about the grade.....How thick is the patio going to be? 4" ? 6 "?
I'm thinking if you have enough grade to plumb it directly to daylight it should work......Your shedding a small roof, probably have a 4" downspout.....can you stay above ground after exiting the new slab and only using pvc?
I'm sure your gonna want some fall on the slab to shed rain n snow away from the house.

You're telling us WHAT you want to do but not WHY. Why is this necessary, and if it's not necessary, why do you want to do it? We don't have any idea the slope of the lawn area. How much pitch to you expect to have on the underground run of pipe and will it be uniform to the end? Is water draining away from the house without issue presently?

Rob - I’m about to do the same thing but multiplied by several gutters Plus a channel drain between new pool and house. How did it work for you? I’m using schedule 40 PVC of course, and considering pouring my patio right up against my crawlspace which would in case the vertical run of PVC going up to my gutters. Just wondering how this would hold up with natural concrete shifting over the years. Of course I could just leave at 12 inch radius of rock around the circle entry point at the patio but I like the idea of solid clean concrete.

How big is the patio gonna be?
How thick? rebar? wire? plastic?

Finished this last year sometime... I used sch 40 pipe (with a wye clean out) under the concrete then about 2 feet into the yard transitioned to dual wall smooth corregated pipe