Answer:
Yes, it is possible to use both an Accounting Integration and PunchOut integration at the same time. Purchase Orders/Bills will sync to your Accounting/ERP Software, but the Vendor must be manually created in your Accounting Software with the exact name as applicable:
Amazon Business (PunchOut)  | 
CDW (PunchOut)  | 
ChemDirect (PunchOut)  | 
DigiKey (PunchOut)  | 
Gertex (PunchOut)  | 
Global Industrial (PunchOut)  | 
Grainger (PunchOut)  | 
Henry Schein (PunchOut)  | 
Home Depot (PunchOut)  | 
Identity Works (PunchOut)  | 
LakeShore Learning (PunchOut)  | 
Marijuana Packaging (PunchOut)  | 
Medline (PunchOut)  | 
MilliporeSigma (PunchOut)  | 
Mouser Electronics (PunchOut)  | 
Office Central (PunchOut)  | 
Original Nations (PunchOut)  | 
Source Atlantic (PunchOut)  | 
Staples Advantage (PunchOut)  | 
Stemcell Technologies (PunchOut)  | 
Thermo Fisher Scientific (PunchOut)  | 
Uline (PunchOut)  | 
VWR (PunchOut)  | 
Zageno (PunchOut)  | 
The Master Data sync will ignore vendors containing "PunchOut" and will not create a duplicate vendor in Procurify.
Additional Information:
If you sync purchase orders and/or inventory items to NetSuite, please also see Syncing Vendor and Account Codes between NetSuite and Procurify (PO and Inventory Sync)
