Yes. Just be careful not to drop it on a energized circuit board!
The strap or the battery? The strap is NOT the degree of "conductive"
you may think it is.
Unless you are dumb enough to have ever or still be using those stupid
"wrist watch strap" designs that were metallic. The cloth ones pass
tests for years as fully functional.
But as for ESD and keeping your products safe from yourself...
The paradigm these days, since fields are also important to abate as
well, is to simply don an ESD smock and be shielded full body. nothing to
drop onto anything, including a charged field. Touch your product
chassis or workbench ground before starting.
Also, your skin is (typically) very dry (comparatively)and you can
accumulate excess electrons (charge) on it with respect to an earth
grounded chassis from your clothing. Moisturize your hands and writs,
since that is where the smocks connect to you at.
Other "charge particulars"
Even an ungrounded chassis is already typically at earth grounded (read
'drained') potential, as it was at one time so grounded and not likely to
have had charges added to it. It will sink your charge. If you only
touch the chassis. You AND the chassis are important to establish being
at the same charge. Do not use electrical ground for ESD abatement
systems. Earth sink points, as in a hard driven ground rod are
preferred.
So, FAIAP even an ungrounded system or chassis is considered "at ground
potential" because it was recently or still is, from an ESD sinking
capacity POV.
Of course there are special situations where an earth ground insulated
(ungrounded) chassis, like one sitting on a table, could build a charge
over the entire chassis with respect to true earth ground, as in a
location where magnetic fields from HV presence or corona or even dry air
in a lightning storm area. Or just dry air.
But for the most part, even an ungrounded chassis is considered "at
ground" and represents the same ESD event sinking capacity as a fully
grounded system.
After many such 'sinking' events, however, one would think that the
chassis itself might have a few extra electrons that might want to jump
into the earth when that contact was re-established.
So back to the smocks.
They now have integrated "wrist straps" because they are long sleeved
and the sleeves have conduction throughout the smock, and the 'ground
lead' gets attached at the left or right pocket, mid smock.
No wrist strap required and no fields are ever present when someone
touches ground as they approach an ESD controlled workstation, and then
hooks up before any examinations or functions utilizing ESD susceptible
componentry is performed. It is all about balance. Typically, the
'ground circuit' of any device or card or circuit you would consider
touching is the ground level of the surface of your bench top, and YOU
yourself.
Otherwise, your PC chassis IS the "ESD safe workstation", and you
either leave it plugged in, or tie the chassis to the electrical fault
line, since you have no ground rod *at* the PC. still, don the smock,
and use the PC chassis as your smock grounding point.
THAT IS THE IMPORTANT MESSAGE OF THIS POST.
For the smocks;
Plug in at a std test station and press the button, and the circuit
from the ground point, through the ESD attachment cord, to the smock
pocket, through the smock, sleeve, and cuff, into your wrist and down
through your finger, back to the button.
A passed test shows that not only is there a path to ground for your
body, but also a 'field shield' over your clothing, all integrated
together to keep you from presenting yourself as an ESD event hazard to
any device with such a susceptibility.
Remember, an ESD event and subsequent failure mode in a product does
NOT require contact, and does NOT always immediately exhibit any evidence
of the damage it has caused.