Hi,
Yes you can (see Help>Data - the last section).
To sum-up because by default Feature Service attachments are limited in size, we don't yet support adding videos when the source is a Feature Service.
But through ArcGIS.com viewer you can edit your data to include a video or any other page (open your webmap in edit mode, edit the field pic_url with the URL of your video). Also if your record has an attribute isVideo, turn it to true, if it doesn't, the URL of your page have to include #isVideo.
Feature Service created from the builder should always have a field named pic_url (alias is 'Picture URL').
If you don't have two fields named pic_url and thumb_url, you won't be able to use video. More details on github here and here.
If you don't want / can't create the Feature Service from the builder, yes you can create those fields yourself, populate them and make sure to have use #isVideo at the end of your video URL.
Using a custom Feature Service is possible but it will require you to read a bit the documentation to make it works. Please take a look at the previous two links I gave you. You need to have two attachments per feature (even for the videos). You need to add pic_url field and also thumb_url.
Alternatively I would recommend that you create a Feature Service from the sample CSV we distribute and start rebuilding your Map Tour from scratch. Add your points with image, then use ArcGIS.com viewer to edit the pic_url when you want a video. if you have an organization, add the CSV as an item and choose to create a service.
When you add pic_url field, you also need to add a thumb_url field. If you don't have these two fields, the attachments are used. If you have these two fields, they are used. If you add only pic_url it doesn't works.
All of that is documented on the previous link. You can't use video if you don't have these two fields.
Ok, I added the thumb_url and now the slide show works for the map point I tried it on. However the photo attachments in the feature service now do not show for the other property map points.
Look at the map. Real Estate Map Tour