Not directly. A fax number is a telephone number and email travels over the internet, so an email addressed to a fax number has nowhere to go and bounces. What makes the answer yes in practice is an online fax service: you email a document to an address the provider gives you, with the recipient's fax number in that address, and the provider's server dials the number and sends the attachment as a fax. The reverse works too, with faxes to your number arriving as email attachments. The service is the bridge, and what it costs is the plan's price, allowance and overage, which the Fax Line Index records from each vendor's pricing page.
Why the two networks do not connect
A fax is a phone call carrying an image: the sending machine dials, the receiving machine answers with a tone, and the pages travel as sound over the line. Email is packets over the internet delivered to a mail server. There is no mail server behind a telephone number and no telephone behind an email address, so neither can reach the other without a service that has one foot in each. That is exactly what an online fax service is, which is why the question has a different answer once you have an account.
How email-to-fax works
You write an email, attach the document, and address it in the provider's format, which puts the recipient's fax number in the address, and the provider transmits it and emails you the transmission report. CocoFax prints Email to Fax and Fax to Email as plan features; every vendor in the catalog sends from email or a web page. Each attached page counts against the plan's allowance: Fax.Plus prints 200 pages a month on Basic at $6.99 with $0.10 per extra page, WestFax 500 pages on Solo at $14.99 with a 3 cent overage.
Receiving faxes as email
The receiving half is the more useful one for most people. A fax sent to your number by any machine arrives in your inbox as a PDF within about a minute of the last page, with the sender's number and the time. That needs a receiving plan with a number, which every paid plan in the catalog includes; FaxZero, the free sender, has no number and cannot receive. For a business that gets faxed orders or referrals, fax-to-email is the reason to pay for a plan at all.
Questions people ask about can you email to a fax number
Can you send an email to a fax number?
Not directly; the email bounces. Through an online fax service, yes: you email the provider's address with the fax number in it and the provider faxes the attachment.
Can a fax be sent to an email address?
Only through a service that receives the fax on a number and forwards it as email, which every receiving plan in the catalog does.
Does emailing a fax cost more?
No. A page sent by email counts against the plan's allowance like any other page; the overage per page is printed beside each vendor's price.