Keto Enol Equilibrium for Claisen Condensation Products
The Claisen reaction yields a product with an acidified proton in $\alpha$-position of carbonyl and ester, right at the same carbon atom of R depicted in blue.

In presence of a base, yes, $\beta$-dicarbonyl compounds undergo deprotonation at their methylene unit to yield a keto-enolate, stabilized by mesomerism with the secound carbonyl group in conjugation. Compare the $pK_a$-values of $\beta{}$-dicarbonyl compounds with ketones, for example (one reference), to estimate if the equilibrium is on the left, or on the right.
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I think cations of the right size and charge equally favour the formation of the keto-enolate.  If you synthesize $\beta$-dicarbonyl compounds, the risk to loose product due to chelation  is lowered if initial work-up is concluded by drying the washed organic phase with sodium sulphate ($\ce{Na2SO4}$), rather than by magnesium sulphate ($\ce{MgSO4}$).