If an insurer imposes loading on a plan, I accept but few months down the road, I cancel the plan and apply with another insurer, would the new insurer be able to find out about this?

Where insurance contracts are concerned, there is this doctrine of 'utmost good faith' where the insurer and policyholder are legally obliged to act honestly toward each other. The policyholder has the duty to voluntarily declare all information critical to the application, especially so if this will affect the underwriting decision of the insurer. Failure to do so may result in the insurer voiding the contract or other legal actions.

During the application of buying a new insurance policy, you would be asked to declare if you have been rejected/have been counter proposed with another new offer by the company (either loading or exclusion). If you choose not to declare it, you are not being honest and company have the rights not to do a payout on your claim in the future as well.