If it is, I need some way to know whether my referent is blessed. However, "sv_isobject" works on a reference. Is there any similar thing works on a referent?

You'll kind of have to clarify what you mean here by "reference" and "referent".

Warning: Blessing involves magic, and I get very antsy around anything to do with (XS) magic.

When you "bless a reference", the magic is attached to the thing referenced, not the reference itself, despite that you need a reference to perform the blessing.

My evidence for this:

#! perl -slw
use strict;

my( $scalar, @array, %hash );
print for \( $scalar, @array, %hash );

=comment Prints
SCALAR(0x2a7c20)
ARRAY(0x2a7c80)
HASH(0x2a7d28)
=cut

bless $_, 'fred' for \( $scalar, @array, %hash );

print for \( $scalar, @array, %hash );

=comment Prints
fred=SCALAR(0x2a7c20)
fred=ARRAY(0x2a7c80)
fred=HASH(0x2a7d28)
=cut

my $newref = \$scalar;
print $newref;

=comment Prints
fred=SCALAR(0x2a7c20)
=cut

my $ref2ref = \\$scalar;
print $ref2ref;
print $$ref2ref;

=comment Prints
REF(0x6e148)
fred=SCALAR(0x2a7c20)
=cut
[download]

Notice how $newRef, and the referent of $ref2ref know that it is the thing they are pointed at that is blessed.

Take that one step further and assign a reference to a new, unblessed thing to a previously blessed reference, and it now knows it refers to a unblessed thing:

$newref = \ 'fred';
print $newref;;

=comment Prints
SCALAR(0x2c7d70)
=cut
[download]

So, the common speech pattern of "a blessed reference" is really a misnomer. What we actually have is "a reference to a blessed thing".

Turning this back to your statement above, sv_isobject() is defined as:

Returns a boolean indicating whether the SV is an RV pointing to a blessed object. If the SV is not an RV, or if the object is not blessed, then this will return false.

Only the referent is blessed, but you have to pass an RV that references it to test whether it is blessed or not.

(Doesn't make a whole bunch of sense to me, but I told you I get antsy around magic. :)

And finally:

Is it harmful if I bless a blessed object?

Re-blessing an object just replaces the package it is blessed into with the new package (or the same). But the old blessing is forgotten. Whether this is a mistake depends upon what you are trying to achieve.