G'day htmanning,

"Is this >=- valid?"

Perl says it is:

$ perl -ce '$no_days = "(TO_DAYS(dateadded)-TO_DAYS(Now())>=-$newdatea
+dded)";'
-e syntax OK
[download]

You appear to have added sufficient parentheses to avoid precedence issues:

$ perl -MO=Deparse,-p -e '$no_days = "(TO_DAYS(dateadded)-TO_DAYS(Now(
+))>=-$newdateadded)";'
($no_days = "(TO_DAYS(dateadded)-TO_DAYS(Now())>=-$newdateadded)");
-e syntax OK
[download]

Is the value assigned to $no_days what you were expecting?

$ perl -e '
    $newdateadded = "NDA";
    $no_days = "(TO_DAYS(dateadded)-TO_DAYS(Now())>=-$newdateadded)";
    print $no_days;
'
(TO_DAYS(dateadded)-TO_DAYS(Now())>=-NDA)
[download]

As you've provided no context for the single statement you posted, it's impossible to tell if it's actually doing what you want.