Yes. If you can afford it!
Here's why:
Prospects are much more likely to enquire/buy from a local site. I.e. Americans are much more likely to enquire/buy from a .com site rather than a .au site
Google will rank your site higher in America if it is on a .com TLD (Top Level Domain), likewise a .au site will rank higher in Australia, etc
The IP address of your site (while minor) does go someway to affecting your Google search results - so ideally the site would also be hosted in that country
Content is king - and should be localised to the country you're targeting. Content is such a critical aspect of your SEO, and needs to be considered for each country individually
Credibility - if you can get your hands on a US phone number and address to plaster all over your .com website - all the better - even if diverting to a messaging service
In-bound links - another critical aspect of SEO is in-bound links. If your local site gets links from other local sites, you're also creating much Google love
Some things to consider:
It can be expensive to build several websites, so try to ensure they're very similar, and also use a CMS platform that supports multiple sites (I.e. Drupal for websites, Magento for eCommerce) to minimise development and maintenance costs
Each of these sites requires their own SEO strategy, link building efforts, etc - which can be expensive. Look to get discounts from your provider for bulk link building
If you can't afford all of this, then consider using sub domains or sub directories for country specific "satellite sites" that are optimised for those countries, then send the traffic back to your main site
There are compromises you can consider - talk to your agency for some advice