Yes, you can add a checklist template to multiple tasks at once. To do so, just open your project on web and go to the Tasks page. Then select the tasks you wish to add the checklist to (hover your cursor over each task and select the checkbox).
Once you've done that, click the red Actions button at the top of the Tasks page. From the Actions menu, place your cursor over the "Add Checklist" option and you will see two more options appear: "New checklist" and "Existing checklist template."
If you want to create a brand new checklist for these tasks, simply select that option and start adding items. If you already have a saved checklist template you want to paste into the tasks, choose the "Existing checklist template" option.
As a note, all tasks that you add a checklist template to will be tagged with the checklist template name. That way, you'll be able to filter and report on tasks with a particular checklist template.