The AsScalarAsync extension is used to asynchronously execute what would otherwise be an "immediate execution" query. These are queries using a .First() or .Sum() or .Contains() or similar operator, which because they will be executed immediately and synchronously, are not allowed in Silverlight.
To use .Contains, or .Any, or .Count, which I think would also work in your scenario, you can do something like the following:
var op = repository.Manager.DBOARD.Select(o1 => o1.ID).AsScalarAsync().Contains(dboard.ID);
var op = repository.Manager.DBOARD.Where(o1 => o1.ID == dboard.ID).AsScalarAsync().Any();
var op = repository.Manager.DBOARD.Where(o1 => o1.ID == dboard.ID).AsScalarAsync().Count();
Note that in all cases an EntityScalarQueryOperation is returned, not a query. This is because the query is still executed immediately.