First. No, the Photos app can not do captioning.
And then, yes, sort of. If you have iOS 8, the new extension feature lets you use features from other apps inside the Photos app for editing. Because you are editing the photo you're not getting a true text caption below the photo, but actually editing the photo with a text tool.
Here is a general overview of how to use them.
First, you have to download the app, and you may need to open it at least once, so it registers it's extensions with iOS. To use the extension in Photos, you open a photo and choose to edit it. Alongside the other editing controls there is a circle with three dots in it. Tap that circle and you'll se your compatible, enabled extensions. If you don't see the extension you want, tap the More icon, with three dots (see the pattern?). You'll get a list of all your compatible extensions and a switch to turn them on/off.
To use the extension, simply tap the icon. It will be the same icon and app name as the app that provided the extension.
The only app/extension I have that I have, that does text, is Camera Plus. I have a couple more extensions on the iPhone, but they are for filters viewing metadata.
Look in the App Store for the "Great Apps for iOS 8" promotion. It's one of those small rectangles between the rows of icons. There's a selection of apps that have photo editing and filter extensions.
Another, quicky solution is Skitch. If you only need to add some text or other quick markups to a picture, Skitch is ideal. It's how I added the text to screenshot you see above. Most screeshots you see on this form, with arrows, text, and blurred areas, are created using Skitch.