Is it safe to send emails from wordpress site to your users?

So I have more than 2k users registered on my site and would like to send some emails to them. My site is hosted in HostGator.
I got a plugin called "Email users" but im worried to send emails from there because my site could go in blacklist or whatever plus when I go to plugin to send those emails there appears this message..

Warning: The number of users () plus overhead exceeds the PHP max_input_vars setting (1000). You will not be able to send email to more than 990 users in one batch. This can be changed by increasing the value ofmax_input_vars setting in the PHP.ini configuration file.

I would like to send the emails from my site because I can specify their name on textbox like

Hello $FirstName , bla bla

Click to expand...

and use my main email admin@mysite.. but Im afraid Its a bad thing.
I would like to hear from experienced people on this thing, if it is safe to send them or it's better to send them from other email marketing sites like mailchimp etc.

you will need to contact Hostgator about it, some hosts don't allow it. Hostgator has a limit on your email sending

just send it over a few days. 500 max per day

I contacted with hostgator and they said that I can send 500 emails hourly and as soon as people who get the email dont report it , it will be okay from their side