Add Task without Date and Time

There is already a way to do that. Use the “Ongoing” event type when you create a sheet. Ongoing sheets don’t require dates, so you can put those type of tasks there. Even in other types of sheets that have dates, times are never required.

From the documentation:

Event Types

When adding a new sign-up sheet, there are four Event Types you can choose from:

Single — This is for an event that happens on just one day. You will only be able to enter one date on the tasks screen that will apply to all items/tasks for this event type.
Recurring — This is for an event that recurs on multiple days, but has the exact same items/tasks needed for each occurrence. For example, our school has Popcorn Fridays almost every Friday, and we need two poppers and one cashier each Friday. On the tasks screen for this event type, there will be a multi-date select box to allow you to set all the dates for this event, and then all of the tasks you enter will show up for each one of those dates. NOTE, it is possible to eventually fill up all the space allocated to this dates field, so if you have an event that recurs a very large number of times, you may need to limit how many upcoming dates you list at one time and deselect old dates after they have passed. We came across this problem with our Popcorn Fridays event for our school, but after I figured out the problem, I more than doubled the available size for this field.
Multi-Day — This is an event that happens across more than one day, but that has different tasks/items needed for each day. For example, we use it for our Book Fairs, where we have a “set up” day and a “take down” day where we just need a certain number of bodies to help, and then for the week of the book fair we need a certain number of cashiers and book finders/floaters for each day. For these Multi-Day event types, each task/item has its own single date picker field to specify the date for that item/task.
Onging — This type of sheet doesn’t have any dates associated with it. These are for more general volunteer type opportunities that don’t have specific date/time type requirements, but are needed at various times throughout the year. For example, you could use it to get volunteers for Yearbook photographers, Webmasters, Art Docents, classroom helpers, etc.