The short answer
No — tags are not added to individual invoices. Tags are configured on the vendor, and every invoice from that vendor automatically picks up the tags.
How tags get onto invoices
Tags are set up in the Vendor Center, in the vendor’s advanced settings, for the locations you choose.
From then on, invoices from that vendor carry those tags automatically — including, retroactively, invoices that have not been exported yet.
If the vendor mapping on an invoice changes or is removed, its tags update to match. Tags always reflect the current vendor setup.

What tags are for
Routing: approval policies can use tag conditions, including "Has No Tag" to catch everything untagged.
Finding things: tags are searchable, so "all invoices tagged Catering" is one search.
Reporting: tags ride along on invoice data for filtering.
If you need per-invoice labels
Because tags mirror the vendor setup, they are the wrong tool for one-off, per-invoice markers. For a single invoice, use a flag with a note (visible to approvers), or the invoice notes field.
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