Is there a way to have something similar to the "draw" toolbar in collector, so you can draw polys and add text to the map?
No, but you could use the measure tool to simulate drawing. This might be a good thing to post on ideas.arcgis.com.
Great suggestion Curtis, found ArcGIS Idea - Enhanced drawing tools for collector based on your post. Be sure to VOTE for those Ideas you'd like to see Esri Teams to consider as feature or product enhancements in a future release. Including complete details such as answers to below questions provides Esri Teams with a clearer picture when reviewing these types of ideas and enhancements.
What is the users workflow and use case?
What is the problem feature X is trying to solve?
What is the benefits or changes that would result from the enhancement?
How do you believe this enhancement may benefit other organizations?
What would you like to use it? Have you look at Explorer for ArcGIS | ArcGIS , which has sketch tool.
Explorer for ArcGIS does have a really nice sketch tool. But is very limited in how you can work with or share sketches after they are created. Almost a great markup tool...
Our users would love this too - they currently take a screenshot of Collector and open it in another app to edit the image, then store those images on their device and refer to them when they go back to a job.
I would like the same Markup Tool in Explorer App to be available in the Collector App. The reason being our field crew currently uses Collector in an offline environment to manage assets. They have requested a way to create simple notes (like the ones available in Markup) without having to manage data on two separate apps. This would also allow us to use our offline base maps in Collector as appose to keeping an up to date Mobile Map Package downloaded on multiple devices.