No can do unless convert the table variables to cell arrays; a double array cannot have anything other than numeric values. A MATLAB table data structure is NOT a spreadsheet although it superficially appears somewhat akin to one...
a=randi([2000 6999],12,1); a(2:2:end)=nan; b=a+1; % some very roughly similar data...
tT=table(a,b) % turn into a table
illustrates don't need a loop nor concatenation to do the first step...
If it really, really, really were important to not have the NaN values showing, one would have to do something like
a=string(a); b=string(b); % turn into nonumeric representations of numbers
a(ismissing(a))=""; b(ismissing(b))=""; % use blanks instead of <missing> indicator
tT=table(a,b)
is rough equivalent of the cell route; a string array can be the null string rather than missing. MATLAB will then display the double-quotes around the values as the visual type indication in the command window.
You would have to fprintf the values with formatting string to get them to look differently.
The cellstr route would be the same idea; it displays "the curlies" around cell values...
tT=addvars(tT,cellstr(tT.a),'After','b','NewVariableName','c')