“(Before the migration), if someone shared a google document to my personal gmail account to open/edit the document, I could not open the document using my company Microsoft company account. Will this change when we rollover to Google Mail for our company?”
SHORT ANSWER: Yes :)
COMPANY GOOGLE ACCOUNT LOGIN: As soon as cutover happens on a predetermined cutover date, you can have your company google account open to edit the google sheet/document. Please see screenshot below for an example which shows me editing a document from my Jones IT work google account (just like you will be able to do with your company work google account). Click on the account on the upper right to login to your company google account. Keep in mind that you also have the power to be logged into your personal gmail if you want to switch between easily by clicking “add account” (as you can see my personal google account is also logged in).
SHARING PERMISSIONS: Keep in mind that the google document must be shared with your work google account (firstname.lastname@example.org) and whomever shared it with you must give you permissions. One thing you can try is sharing documents with yourself from your personal google account to your company google account. Please see below screenshot. Click on the blue “Share” button on the upper right while the document is open. You will get the “Share with others” popup where you can enter the email addresses of the people you want to share and their permissions (can edit, can comment, or can view).
SHAREABLE LINKS (Bonus material if you’re curious): It’s also important to know about sharing documents with links. Once you click the blue “Share” button on the upper right while the document is open and the “Share with others” popup opens, you can click the button “Get shareable link,” which will copy the link to your clipboard and let you paste that link wherever you want to share it (e.g. in email). But please beware that the default security is that “anyone at company with the link can view” and if you want to change those settings for that specific document you must click on where it says “Anyone with the link can…”. This will will bring up a menu as seen in first below screenshot "Share with others." If you need more options (like sharing outside company & public), click on “More…” and you will then see more options as seen in second below screenshot "Link sharing."