If you control both ends of this. Lets say the CRM is yours in QuickBase and the SQL Server which is creating the SSRS data is yours then yes.
Setup a web hook in CRM, connect it to a trigger of your choice. Trigger of your choice means, when a check box is checked activate webhook, or when a button is clicked (which if you do button option you must have button trigger a hidden checkbox which will then trigger web hook) The webhook in Quickbase will send to the end point of your choice.
To hit an endpoint you need the endpoint URL, an example of this is
https://subdomainname.quickbase.com/db/dkjfalk343 that is a fake URL, but the subdomainname is your companies name most of the time, and the last part of the URL is the specific spot you are trying to target, like a table, or form.
You will need a user token most likely which be a header inside of your webhook in Quickbase, I personally would use JSON instead of XML to send your data. Then inside you select which fields in Quickbase to send.
EX:
{
"imnamingthisvariablehere": "[quickbasefield]",
"anothervarisbleimnaminghere": "[quickbasefield]",
"triggerMyServerResponse": "True"
}
This will send over any fields in Quickbase you want, with the variable names you are attaching to them.
From the other side, your server which is making the SSRS, you create another trigger, which activates when something you chose happens. So from Quickbase you send a field over like triggerMyServerResponse, which true will check an unchecked box. so your webhook on your server will activate when that checkbox is checked from Quickbase.
Then you repeat the process.
Make a user token in Quickbase (user settings, preferences, user token)
find the URL of the table and form you want to hit in Quickbase (record ID# hits the record in the table and the /db/dbid hits the table and the subdomainname.quickbase hits the CRM. map out every field in the Quickbase record you are wanting to populate with their Field_ID numbers. Then POST the data back to your CRM.
This works only if you have control of both ends, the CRM and the server (Which im assuming you have because you said SSRS which is part of Microsoft SQL)
I know this is probably really confusing still, If you have more questions feel free to ask and I can try and help more. This works because you don't have to see the payload, and you do not manipulate any data on API calls, its just a POST which triggers another POST.