You can created a logo in illustrator, save it to your desktop. And you can place that logo on to an indesign layout (s) for future use. Just remember to package every time so a new instance of that logo go with that particular layout/project.
If you are and adobe cloud subscriber you can do an even better set up and create a library for each of your brands or clients. add the logo to it from illustrator and the swatches that go with that brand. This way it will be save in every one of your adobe applications and ready to be dragged into your layouts/projects from the library panel.
If is fine if you want to keep a graphics in your desktop for use and re-use, but do remember to package your files for catalog and archive purposes. If you have to hand off things to somebody else and or the folder changes locations ( form a local drive to share drive) you may have missing links.
here is a link to how to package your files:
Package files for handoff |
Ps: be mindful of how many things you keep on your desktop. Remember that the more stuff you have on your desktop the more stuff your computer has to remember to keep available on the desktop. To improve your performance it is better to catalog things in your documents folder and create a shortcut to it on your desktop.
I hope this helps