Would PaymentIntent error out during creation if not enough funds or not payment method, etc?

const stripe = require('stripe')(secret_key);

const paymentIntent = await stripe.paymentIntents.create({
  customer: customer_id,
  amount: 2000,
  currency: 'usd',
  automatic_payment_methods: {enabled: true},
});

If I create a PaymentIntent like the above via Node, will it check for whether or not the customer actually has the resources to fulfill this payment amount?

No. PaymentIntent will need to be confirmed (passing confirm: true) to actually attempt to charge this customer_id.

Note that you shouldn't share your secret key, even a Test mode one, in a public space like this.