Rendering to texture, then using texture on next frame...

Hello, I’m FBO rendering to quite large textures, often with complex shaders. But I don’t need them immediately, so would it be better to double buffer them to be used in the next frame, or doesn’t it really matter? I was thinking that if they were used immediately then it may cause a delay while waiting for texture completion.
I hope that makes sense,

Are you experiencing any artefacts or only speculating?

Thanks for replying.
I’m just getting delays on slower graphics cards (laptop). A small number of textures are 2048x2048 in size, and I was wondering if the pipeline was halted while the texture was being made so it can be rendered at the next stage.
I’m doing texture streaming, so it’s not essential the texture is displayed the very same frame loop.