Can CloudFormation add existing policy to existing role?

There is no native mechanism to take existing role and existing policy and attach one to the other in CloudFormation. Since CFT is about creating resources, you need to be creating at least one of the two resources. You've probably seen this support question that covers the supported scenarios: How can I attach an IAM managed policy to an IAM role in AWS CloudFormation?

To accomplish what you want, you can create a lambda-backed custom resource passing in the ARN for the existing policy and role name with the function calling the IAM AttachRolePolicy API to do this.

Here is a working example I threw together. On stack delete, it will detach the policy that was attached. On stack update, it will detach the old policy from the old role and then attach the new policy to the new role allowing you to change the existing policy, existing role or both

AWSTemplateFormatVersion: '2010-09-09'
Parameters:
  ExistingPolicyArn:
    Type: String
    Default: arn:aws:iam::aws:policy/AmazonEC2ReadOnlyAccess
  ExistingRoleName:
    Type: String
    Default: ExistingRole
Resources:
  IamXtachPolicyRoleLambdaRole:
    Type: AWS::IAM::Role
    Properties:
      AssumeRolePolicyDocument:
        Statement:
        - Effect: Allow
          Principal:
            Service: lambda.amazonaws.com
          Action: sts:AssumeRole
          Condition: {}
      Path: /
      ManagedPolicyArns:
        - arn:aws:iam::aws:policy/service-role/AWSLambdaBasicExecutionRole
      Policies:
        - PolicyDocument:
            Statement:
              - Action:
                  - iam:DetachRolePolicy
                  - iam:AttachRolePolicy
                Effect: Allow
                Resource:
                  - !Sub "arn:aws:iam::${AWS::AccountId}:role/*"
            Version: 2012-10-17
          PolicyName: aws-app-iam-xtach-policy

  IamXtachPolicyRoleLambda:
    DependsOn: IamXtachPolicyRoleLambdaRole
    Type: AWS::Lambda::Function
    Properties:
      Handler: index.lambda_handler
      Timeout: 30
      Role: !GetAtt IamXtachPolicyRoleLambdaRole.Arn
      Runtime: python3.8
      Code:
        ZipFile: |
          import logging
          import boto3
          import cfnresponse

          logger = logging.getLogger()
          logger.setLevel(logging.INFO)

          def lambda_handler(event, context):
            
            def attach_policy(policyArn, roleName):
              return iam.attach_role_policy(
                PolicyArn=policyArn,
                RoleName=roleName,
              ) 
            
            def detach_policy(policyArn, roleName):
              return iam.detach_role_policy(
                PolicyArn=policyArn,
                RoleName=roleName,
              ) 

            try:

              iam = boto3.client('iam')
            
              existingPolicyArn = event['ResourceProperties'].get('ExistingPolicyArn')
              existingRoleName = event['ResourceProperties'].get('ExistingRoleName')
            
              if event['RequestType'] == 'Create':
                response = attach_policy(existingPolicyArn, existingRoleName)
              elif event['RequestType'] == 'Delete':
                response = detach_policy(existingPolicyArn, existingRoleName)
              elif event['RequestType'] == 'Update':
                oldExistingPolicyArn = event['OldResourceProperties'].get('ExistingPolicyArn')
                oldExistingRoleName = event['OldResourceProperties'].get('ExistingRoleName')
                response = detach_policy(oldExistingPolicyArn, oldExistingRoleName)
                response = attach_policy(existingPolicyArn, existingRoleName)

              result = cfnresponse.SUCCESS
              
            except Exception as error:
              logger.exception(error)
              response = {
                'status': 500,
                'error': {
                  'type': type(error).__name__,
                  'description': str(error),
                },
              }

              result = cfnresponse.FAILED 

            finally:
              cfnresponse.send(event, context, result, response, {})
              return
 
  AttachExistingPolicyToExistingRole:
    DependsOn: IamXtachPolicyRoleLambda
    Type: Custom::IamXtachPolicyRoleLambda
    Properties:
      ServiceToken: !GetAtt IamXtachPolicyRoleLambda.Arn
      ExistingPolicyArn: !Ref ExistingPolicyArn
      ExistingRoleName: !Ref ExistingRoleName