They may if you go to a full-service Safelite installation facility (you may or may not have that available in your locale) - they cannot with an in-the-field installation, period.
Safelite will also source and install genuine Honda windshields - but if you don't specify that up-front you may or may not get it - "OEM replacement" does not guarantee "Genuine Honda" with Safelite - ya gotta be careful in your specification of what you want. You must call Safelite to discuss all the relevant options they offer in your area - you cannot get the 'full-poop' using their online systems for estimating / making an appointment. It's not that they're maliciously trying to screw you, it's just that they have lots of options and most of their customers are more interested in 'quick and cheap' than "Genuine [mfr]" glass.
Shop around either in-person or on the phone; I've had great service from Safelite in the past on other vehicles with no problems whatsoever (always specifying and receiving genuine OE glass and always taking my vehicle to their huge service facility in Austin). But when I shopped for my Ridgeline I found that the turnkey price was less through my local Honda Dealer; they acknowledged that they provide the Honda glass, a subcontractor installs it in one of their service-bays at the Honda Dealer, then the Honda Dealer techs do the recalibration of all the ADAS systems. That Honda Dealer has certain days set-aside for windshield replacements by appointment only. All of the warranty for both install and calibration is backed by the Honda Dealer - the customer has no dealings directly or indirectly with the subcontractor.
All that can vary depending on the local dealer (both Honda and Safelite). Ya just gotta get off the forum and on the phone to the folks you will actually be dealing with to get the low-down applicable to your locale.
