If the browser can access the site, it means IP blocking software is not preventing access, but it does not necessarily mean a firewall isn't blocking IDM because firewalls block or allow programs to access the net, not necessarily specific sites. So just because a browser can access the site doesn't necessarily mean the firewall isn't blocking IDM from doing the same. My firewall blocks or allows each program separately. So Firefox is allowed to access all sites and IDM is also. But if IDM wasn't, it wouldn't be able to access any sites even though my browser can.
As to how you can check, I only know how the particular firewall I use (Comodo) works and I doubt that would apply to you. But in Comodo, one can check the firewall's "network security policy" to see which programs are being blocked and which are allowed to access the net.
Assuming you are using the Windows Firewall, I suppose there is probably a list (somewhere within the firewall application) of programs that are blocked and programs that are allowed (it may be an exclusion list of programs that are excluded from being blocked). You would need to find and check those lists to see if IDM is being blocked or allowed. However, if IDM can access any sites, it's not being blocked by the firewall. Hopefully, someone who is more familiar with the Windows Firewall will offer some additional information.
