Traditionally historians have portrayed Harrison's limited presidency as being dominated by other politicians. Notably his brief presidency is viewed as competition between Webster at state and Clay in congress, fighting over the president. At the time of Harrison's death Webster appeared to be winning the battle, although the administration was still heavily dependent on Clay to enact congressional legislation (and in a short period of time he did pass a tremendous amount of legislation). Some more recent histories note Harrison's reject this narrative and place more emphasis on Harrison's comparatively active role in the 1840 campaign. Harrison also had lengthy executive service both in the military and as governor, which is often seen as a major qualifier for the presidency. Harrison also enjoyed a brilliant Secretary of State in Webster and Whig domination of Congress lead by one of the greatest political figures in American history in Clay. Ultimately I think Harrison's presidency was far to short to be able to say with any certainty if he would have even been a good president (and modern connotations of "good" conflict with antebellum understandings of "good", for instance Harrison pledged to only serve one term would likely have little meaning to a modern audience but was viewed as a tremendous pledge coming after Jackson's "Tyrannical rule") what I think we can say is that Harrison certainly had the tools to be an effective president, especially in the arena of foreign policy in which the executive traditionally had the most control.

Edit: In regards to Webster- We don't know

Webster was a talented politician and a very effective secretary of state but these two things do not a good president make, notably examples being the two Adams presidents or Van Buren. Webster would have had some large problems in particular his lack of executive experience and the fact that he repeatedly failed to wrest control of the Whig party from Clay. Throughout the antebellum period Webster's support would be largely limited to the Northeast.