The answer is yes and you will need laser goggles/glasses to protect you eyes--even if you can not see the IR beam or dot at all.
You very obviously have no clue at all about lasers and laser safety. You would be well advised to study both prior to building or buying anything.
Lasers are not play toys for children--they are dangerous for several reasons.
An accidental hit to you eyes of less than 0.25 second can leave you permanently blind forever--same goes for anyone around you that gets hit in the eye
Those diodes were and idiotic choice if you want a visible burning laser.
808nm is normally outside of the human visual range but most people can "see" 808nm laser light in the dark depending on the spectral sensitivity of their eyes and the number of photons hitting the retina at the same time--then you can see a weak/dim red dot. For explanation see:
https://source.wustl.edu/2014/12/the-human-eye-can-see-invisible-infrared-light/
Will be as dangerous and any 500mW laser of even the brightest visible wavelength And no you will not see the beam
You ought to try learning at least something about lasers, wavelengths, and human vision before you dump money on useless waste of time items--unless you want to forge ahead "blindly" and make an invisible laser anyway. In that case since you have no clue about what you are doing you then become and accident looking for a place to happen--a danger to yourself and others.
Those 808nm diodes are used in making DPSS 532nm green lasers requiring a double crystal system to convert the IR to a visible wavelength.
At least read about 532nm green laser pointers here see:
https://en.wikipedia.org/wiki/Laser_pointer
Read up on all aspects of laser safety on this excellent web site:
Laser Pointer Safety - A comprehensive resource, for safe and responsible laser use
These are ok low priced laser goggles/glasses but the pair you need is $59.99:
https://www.survivallaserusa.com/Safety_Goggles/cat1667093_1527285.aspx
NOTE: Ask your parents for permission, first, before you do anything if you are under 18. They are responsible for you and everything/anything you do including any damage/injury to yourself or other people.