Hi, I´m Ansoli, I am interested in your project. I currently manage / monitor the AWS account for a company of online education in Perú.
The configuration of the AWS services and the migration of all your files and database will not have problems, so if you should leave the site maintenance for a while is necessary for the database.
The disadvantage is that your application must have the ability to write in amazon S3 , which means that you would have to edit the code to update it to work properly.
I recommend that the developer of your application will edit it and I will provide the information and access to do so.
If you have your own domain , the SEO of your website will not be affected
Please make me all your concerns to agree with exactitude support the migration of your website.
Regards