You can't really design anything "without regard for color profile" unless you don't care how the colors reproduce. Color profiles are essential to maintaining consistent and accurate output. That said, color space (RGB, CMYK, Lab or a combination) is not important in modern press workflows.
InDesign recognizes the color profiles of all placed images (sRGB, Adobe RGB, ProPhoto RGB, etc.). When you export to PDF (never PNG or JPG if you're going to press -- never, ever), InDesign uses exactly the same code as Photoshop to convert RGB images to the output color space and color profile, if you output to a legacy PDF format.
That's why there is no need to convert images to CMYK before placing them in an InDesign layout. It doesn't do any harm, most of the time, but there are no advantages. Converting RGB images to CMYK adds time and two extra opportunities for error: updates to the RGB image not being kept in sync with the CMYK version, and loss of color gamut if you use the wrong CMYK color profile in the conversion.
The most modern RIPs (software that performs color separation and rasterization of artwork for negatives or printing plates) use PDF/X-4 or /X-5, which allow for live transparency, RGB images and CMYK illustrations/text. With these workflows, every element in the layout must be tagged with a color profile, since the conversion is done in the RIP, not in creating the PDF. (This kind of profile-tagged PDF is more common in Europe, where color accuracy seems to matter more than here in the US.)
Finally, to take up your mention of jpeg and png:
There is no such thing as a CMYK PNG. PNG is a format created explicitly for the web, and a PNG file doesn't even contain metadata to indicate its color profile, since that is assumed to be sRGB, the web standard.
Neither jpg nor png are suitable as output to send to press, because all vector information (such as text) is rasterized at whatever output resolution is specified, usually 300 ppi. That's not nearly good enough for press. Live text and vector information is rasterized at 2400 to 2800 dpi in a printing plant's RIP. Even a desktop printer has better resolution than 300 dpi, so you would be reducing the quality of your output to no good purpose.
Neither jpeg nor png can contain spot (e.g. Pantone solid) colors.
If you want to print your InDesign layout to a desktop printer, print it directly from InDesign, or export to PDF and print that. Your desktop rpinter is an RGB device, so all colors will be converted to RGB in that workflow.