1. No, you can't use sysdate in check constraints.

Why?

All rows in a table for an enabled constraint must return true for its expression.

But sysdate is non-deterministic. You can get a different result every time you call it. So the outcome (true/false) can (will) change over time. So Oracle can't guarantee that the expression is always true for every row.

See:

http://docs.oracle.com/database/121/SQLRF/clauses002.htm#SQLRF52205

2. You could run a select with no where clause and see how many rows are returned. e.g.:

declare
  type t is table of hr.employees%rowtype index by pls_integer;
  emps t;
begin
  select * 
  bulk   collect
  into   emps
  from   hr.employees;
   
  dbms_output.put_line('Rows (sql rowcount) ' || sql%rowcount);
  dbms_output.put_line('Rows (collection count) ' || emps.count);
end;
/

Rows (sql rowcount) 107
Rows (collection count) 107

I'm not sure why you'd want to do this though. Why do you want a method other than count?